In a large bowl, combine 3 3/4 cups of the flour, the sugar, yeast and salt; whisk to blend, then make a well in the center.
In a small saucepan over medium heat, melt 5 tbsp. butter. Add the milk and heat to exactly 115 degrees , 1 to 2 minutes. Add the warm milk and beaten eggs to the well; stir with a wooden spoon to make a shaggy dough.
Mound 1/2 cup flour off to the side of a wooden board or work surface. Lightly dust the board, turn out the dough, then knead, dusting and kneading with flour, until dough is slightly sticky, smooth and elastic, about 7 minutes. Oil a clean, large bowl, add the dough and turn to coat. Cover the bowl snugly with plastic wrap and let the dough rise in a warm, draft-free area until double in bulk, 30 to 45 minutes.
Preheat the oven to 350 degrees . Grease a large baking sheet; in a cup, melt the remaining 3 tbsp. butter in the microwave. Dust the work surface with flour, turn out the dough and cut in half. Roll out one dough half to an 8-by-12-inch rectangle, then, using a pastry wheel or large knife, cut lengthwise into two 4-by-12-inch strips. Brush each strip with butter, then fold the long side up 1 inch, leaving 2 inch of the buttered dough exposed. Cut each of the folded strips crosswise into six 2-by-3-inch rectangular pieces (for a total of 12 rolls). Arrange the rolls, in slightly overlapping rows, on the prepared sheet. Repeat with the remaining dough and melted butter. Cover the rolls loosely with plastic wrap and let rise until doubled, about 30 minutes.
Bake the rolls until puffed and golden, about 18 minutes. Let the rolls cool on the pan for at least 10 minutes; serve warm. Rolls can be made 3 days ahead: Wrap in parchment, then foil and freeze. Thaw for 30 minutes at room temperature, then warm in the oven at 325 degrees for 5 minutes.