Preheat oven to 400 degrees. Wrap the garlic head in a piece of aluminum foil, and roast it until the garlic cloves are soft, 30 to 40 minutes. When garlic head is cool enough to handle, squeeze out the soft garlic from each pod. Place the soft garlic in a small bowl, and stir until a puree forms. Finely chop the large sage leaves, and stir them into the garlic puree; set the filling aside.
Place 1/2 cup warm milk in a small bowl, and sprinkle the yeast over the top. Set aside to dissolve, about 5 minutes.
Pour the remaining 3/4 cup milk into a medium saucepan, set over medium-high heat, and bring just to a boil. Cut 6 tablespoons butter into small pieces. Remove the pan from the heat, and stir in the butter pieces, the sugar, and the salt. Stir until the butter has completely melted. Set pan aside.
Place 4 1/2 cups flour in the bowl of an electric mixer. Using your hand, make a well in the center of the flour. Place the yeast mixture, the butter mixture, and the eggs in the well. Fit the mixer with the dough hook, and, with the machine on low speed, blend just until the mixture starts to come together, about 2 minutes.
Transfer the dough to a lightly floured surface. Knead until the dough becomes soft and smooth and is no longer sticky, 5 to 10 minutes, adding the remaining cup flour as needed. Lightly butter a bowl and an 11-by-17-inch baking pan. Place the dough in the buttered bowl. Turn the dough so that it is lightly coated with butter, and cover dough with a clean kitchen towel. Let dough rise in a warm place until doubled in size, about 1 1/2 hours. Punch down dough, and let rest 10 minutes.
Melt the remaining 4 tablespoons butter. Divide the dough in half. Roll out one piece on a lightly floured surface, keeping the second piece covered, forming a 10-by-12-inch rectangle; trim the edges as needed. Cut each rectangle lengthwise into five 2-inch-wide strips. Cut each strip into three 4-inch-long rectangles. Working with one rectangle at a time, brush half of it with melted butter, and spread about 1/8 teaspoon garlic-sage filling in a thin layer over the melted butter. Fold rectangle in half, leaving a 1/2-inch overhang at the bottom. Transfer the roll to the prepared baking pan. Repeat forming and making rolls, arranging them on the baking pan so they overlap slightly. Roll out remaining half of covered dough, and form remaining rolls. Cover the baking pan with a clean kitchen towel.
Let the rolls proof in a warm place until they have doubled in size, about 30 minutes. Brush the top of each roll with melted butter and arrange 3 sage leaves on top. Bake rolls until they become golden brown on the tops, 15 to 20 minutes. Serve.