To make the brioche dough: In a stand mixer fitted with the dough hook, combine the all-purpose flour, bread flour, yeast, 1/3 cup plus 1 tablespoon sugar, 1 tablespoon salt, 1/2 cup cold water, and 5 of the eggs. Beat on low speed for 3 to 4 minutes, or until all of the ingredients have come together. Stop the mixer as needed to scrape the sides and bottom of the bowl to make sure all of the flour is incorporated into the wet ingredients. Once the dough has come together, beat on low speed for another 3 to 4 minutes. The dough will be very stiff and seem quite dry.
On low speed, add 1 cup plus 6 tablespoons (or 2 3/4 sticks) of the butter, cut into small pieces, one piece at a time, mixing after each addition until it disappears into the dough. Then, continue mixing on low speed for about 10 minutes, stopping the mixer occasionally to scrape the sides and bottom of the bowl. It is important for all of the butter to be mixed thoroughly into the dough. If necessary, stop the mixer occasionally and break up the dough with your hands to help mix in the butter.
Once the butter is completely incorporated, turn up the speed to medium and beat for another 15 minutes, or until the dough becomes sticky, soft, and somewhat shiny. It will take some time to come together. It will look shaggy and questionable at the start and then eventually will turn smooth and silky. Then, turn the speed to medium-high and beat for about 1 minute. You should hear the dough make a slap-slap-slap sound as it hits the sides of the bowl. Test the dough by pulling at it: it should stretch a bit and have a little give. If it seems wet and loose and more like a batter than a dough, add a few tablespoons of flour and mix until it comes together. If it breaks off into pieces when you pull at it, continue to mix on medium speed for another 2 to 3 minutes, or until it develops more strength and stretches when you grab it. It is ready when you can gather it all together and pick it up in one piece.
Place the dough in a large bowl or plastic container and cover it with plastic wrap, pressing the wrap directly onto the surface of the dough. Let the dough proof in the refrigerator for at least 6 hours or up to overnight. At this point, you can freeze the dough in an airtight container for up to 1 week.
To make one loaf into plain brioche: Divide the dough in half. Reserve one half for the Sticky Stick Buns. Line the bottom and sides of s 9 by 5 inch loaf pans with parchment, or butter the pan liberally. Press one piece of dough into about a 9-inch square. The dough will feel like cold, clammy Play-Doh. Facing the square, fold down the top one-third toward you, and then fold up the bottom one-third, as if folding a letter. Press to join these layers. Turn the folded dough over and place it, seam-side down in one of the prepared pans.
Cover the loaf lightly with plastic wrap and place in a warm spot to proof for about 4 to 5 hours, or until the loaves have nearly doubled in size. They should have risen to the rim of the pan and be rounded on top. When you poke at the dough, it should feel soft, pillowy and light, as if it’s filled with air – because it is! At this point, the texture of the loaves always reminds me a bit of touching a water balloon. Position a rack in the center of the oven, and heat the oven to 350 degrees F.
In a small bowl, whisk the remaining egg until blended. Gently brush the top of the loaf with the beaten egg.
Bake for 35 to 45 minutes, or until the top and sides of the loaf are completely golden brown. Let cool in the pan on a wire rack for 30 minutes, then turn the loaf out of the pan and continue to cool on the rack.
The bread can be stored tightly wrapped in plastic wrap at room temperature for up to 3 days (if it is older than 3 days, try toasting int) or in the freezer for up to 1 month.
To make the goo: In a medium saucepan, melt 3/4 cup (1 1/2 sticks) butter over medium heat. Whisk in 1 1/2 cup brown sugar until the sugar dissolves. Remove from the heat and whisk in the honey, cream, 1/3 cup water, and 1/4 teaspoon salt. Let cool for about 30 minutes, or until cooled to room temperature. You should have about 2 cups. (The mixture can be made up to 2 weeks in advance and stored in an airtight container in the refrigerator.).
To make the rolls: On a floured work surface, roll out the second piece of dough into a rectangle about 16 by 12 inches and 1/4 inch thick. It will have the consistency of cold, damp Play-Doh and should be fairly easy to roll. Position the rectangle so a short side is facing you.
In a small bowl, stir together 1/4 cup brown sugar, 1/3 cup granulated sugar, the cinnamon, and half of the pecans. Sprinkle this mixture evenly over the entire surface of the dough. Starting from the short side farthest from you and working your way down, roll up the rectangle like a jelly roll. Try to roll tightly, so you have a nice round spiral. Even off the ends by trimming about 1/4 inch from each one.
Use a bench scraper or a chef's knife to cut the roll into 8 equal pieces, each about 1 1/2 inches wide. (At this point, the unbaked buns can be tightly wrapped in plastic wrap and frozen for up to 1 week. When ready to bake, thaw them, still wrapped, in the refrigerator overnight or at room temperature for 2 to 3 hours, then proceed as directed.).
Pour the goo into a 9-by-13-inch baking dish, covering the bottom evenly. Sprinkle the remaining pecans evenly over the surface. Place the buns, a cut side down and evenly spaced, 2-by-4 inches, in the baking dish. Cover with plastic wrap and place in a warm spot to proof for about 2 hours, or until the dough is puffy, pillowy, and soft and the buns are touching.
Position a rack in the center of the oven, and heat the oven to 350 degrees.
Bake for 35 to 45 minutes, or until golden brown. Let cool in the dish on a wire rack for 20 to 30 minutes. One at a time, invert the buns onto a serving platter, and spoon any extra goo and pecans from the bottom of the dish over the top.
The buns are best served warm or within 4 hours of baking. They can be stored in an airtight container at room temperature for up to 1 day, and then warmed in a 325-degree-F oven for 6 to 8 minutes before serving.