How to Make It
Prepare the rolls In the clean bowl of a stand mixer, combine the milk, egg and yeast and let stand until foamy, about 5 minutes. Attach the dough hook and beat at low speed until combined. Add the flour, salt and sugar and beat at medium speed until combined, about 2 minutes. With the mixer on medium speed, gradually add the butter and mix until the dough is smooth. Transfer to a parchment paper–lined baking sheet, cover with plastic wrap and flatten with your palms. Refrigerate the dough overnight.
Meanwhile, make the garlic butter In a medium saucepan, melt 1 1/2 sticks of butter over moderately low heat. Add the garlic and cook, stirring frequently, until soft and lightly browned, about 12 minutes. Transfer to a food processor and let cool slightly, then puree until smooth. Let cool.
In a stand mixer fitted with the paddle, beat the remaining 4 sticks of butter with the cheese, salt and pepper until smooth. With the mixer on low, gradually add the cooled garlic butter and beat until smooth. Scrape the mixture into a pastry bag fitted with a 1/4-inch round tip.
Line a large baking sheet with parchment paper. On a lightly floured work surface, roll out the dough to a 9-by-12-inch rectangle. Using a large knife, cut the dough into three 4-by-9-inch strips. Arrange 1 strip of dough so that the long side is facing you. Pipe a strip of the garlic butter lengthwise onto the top half, then fold the top edge over the butter to the center, pressing to seal. Pipe another strip of the garlic butter along the seam. Fold the bottom edge of the dough over the butter, pinching to seal. Cut the stuffed dough into 8 pieces and arrange seam side down and 1/2 inch apart on the prepared baking sheet. Repeat with the remaining 2 strips of dough and the garlic butter to form a total of 24 garlic bread rolls. Cover loosely with a large sheet of greased plastic wrap and let rise in a warm place until doubled in bulk, about 2 hours. Reserve the remaining garlic butter.
Meanwhile, make the topping In a stand mixer fitted with the paddle, beat the flour with the cheese and salt until mixed. With the machine on low, gradually beat in the butter until evenly moistened and crumbly.
Preheat the oven to 375°. In a small saucepan, melt the reserved garlic butter over low heat. Brush the rolls with the melted garlic butter and sprinkle with the topping. Bake for about 40 minutes, until golden and puffed. Serve warm.