"These flaky morning buns are an interesting change from traditional cinnamon rolls. Making the croissant-style dough from scratch is a long labor of love, but for a dedicated baker the results are well worth the work."
Remove 1 1/2 cups butter from refrigerator and let stand for 10 minutes at room temperature. Stir 1 1/2 cups cold butter and 2 tablespoons flour together in a bowl with an electric mixer on slow speed until flour is just incorporated. Turn butter mixture out onto aluminum foil and shape into a 6-inch square. Wrap with aluminum foil and refrigerate.
Dissolve yeast and 3 tablespoons white sugar in warm water in a bowl. Let stand until yeast softens and begins to form a creamy foam, about 5 minutes.
Stir 3 cups flour, milk, 2 tablespoons melted butter, and yeast mixture together in a bowl. Add remaining 1 cup flour, 1/3 cup at a time, stirring to form a soft dough. Turn dough out onto a lightly floured surface and knead until smooth, about 5 minutes. Place dough in a bowl, cover bowl with plastic wrap, and refrigerate for 1 hour.
Remove dough and butter-flour square from refrigerator. Turn dough out onto a lightly floured surface and roll into a 10x10-inch square. Place unwrapped butter square on the diagonal in the center of the dough square. Fold dough corners to overlap in the center of the butter square. Pinch dough edges together to seal.
Roll folded dough into an 8x18-inch rectangle. Fold dough into thirds from long ends to the center, as if folding a letter. Roll and repeat the fold thirds folding process. Wrap dough in plastic wrap and refrigerate for 1 hour. Repeat the rolling, folding, and refrigerating process twice, and finish by refrigerating the dough for 4 hours or up to overnight.
Stir 1 cup brown sugar, 1 cup white sugar, and 3 tablespoons together in a bowl.
Brush 24 muffin cups with melted butter and sprinkle each cup with ground cinnamon, turning to coat sides of muffin cups.
Roll dough into an 10x36-inch rectangle. Brush with melted butter and sprinkle with cinnamon-sugar mixture, reserving 1/2 cup. Starting at the wide end, roll up the dough and pinch edge to seal. Cut roll into 24 pieces. Place pieces in prepared muffin pans; let rise until doubled in size, about 1 hour.
Preheat oven to 375 degrees F (190 degrees C).
Bake in the preheated oven until a toothpick inserted in the center of the bun comes out clean, about 25 minutes. Roll the top of each bun in reserved 1/2 cup cinnamon-sugar mixture and set on a wire rack to cool.