Prepare Dough: In cup, combine warm water, yeast, and 1 teaspoon granulated sugar; stir to dissolve. Let stand 5 minutes, or until foamy.
In large bowl, with mixer at low speed, blend yeast mixture with milk, butter, salt, egg yolks, 3 cups flour, and remaining 1/4 cup granulated sugar until blended. With wooden spoon, stir in 3/4 cup flour.
Turn dough onto lightly floured surface and knead about 5 minutes, until smooth and elastic, working in about 1/4 cup more flour as necessary just to keep dough from sticking.
Shape dough into ball; place in greased large bowl, turning dough over to grease top. Cover bowl and let dough rise in warm place (80 to 85 degrees F) about 1 hour.
Meanwhile, prepare Filling: In small bowl, combine brown sugar, currants, and cinnamon. Reserve melted butter.
Prepare Topping: In 1-quart saucepan, heat brown sugar, butter, corn syrup, and honey over low heat, stirring occasionally, until butter has melted. Grease 13- by 9-inch metal baking pan; pour melted brown-sugar mixture into pan and sprinkle evenly with pecans; set aside.
Punch down dough. Turn dough onto lightly floured surface; cover and let rest 15 minutes. On lightly floured surface, with floured rolling pin, roll dough into 18- by 12-inch rectangle. Brush dough with reserved melted butter and sprinkle with currant mixture. Starting at one long side, roll up dough jelly-roll fashion; place, seam side down, on surface. Cut dough crosswise into 20 slices.
Place slices, cut side down, on topping in baking pan in 4 rows of 5 slices each. Cover pan and refrigerate at least 12 or up to 20 hours.
Preheat oven to 375 degrees F. Bake buns 30 minutes, or until golden. Remove pan from oven. Immediately place serving tray or jelly-roll pan over top of baking pan and invert; remove baking pan. Let buns cool slightly to serve warm or cool completely to serve later.