Combine warm milk, sugar, egg, egg yolk, and yeast in a stand mixer bowl. Let sit until foamy, about 3 minutes.
Add flour and salt. Knead on medium-low with the dough hook for 2 minutes until shaggy.
Add softened butter one piece at a time, mixing after each addition. Knead until dough is smooth and pulls away from the bowl, about 5 minutes total.
Transfer dough to a greased bowl, cover, and let rise until doubled, about 1½ hours.
Grease a 12-cup muffin tin. Deflate dough and divide into two equal balls.
Roll one ball into a 15x12-inch rectangle. Cut vertically into 6 strips, each 2½ inches wide.
Brush 5 strips with 1 tablespoon melted butter. Stack them, unbuttered strip on top, and cut crosswise into 6 stacks.
Place each stack cut-side up in a muffin cup. Repeat with remaining dough and 1 tablespoon melted butter.
Cover and let rolls rise until doubled, 1¼ to 1½ hours. Heat oven to 350°F with rack in upper-middle position.
Bake until golden brown, 20–25 minutes, rotating tin halfway through. Brush with remaining 4 tablespoons melted butter.
Cool in tin for 5 minutes, then transfer to a wire rack.