In bowl of stand mixer, combine milk, sugar, egg and yolk, and yeast and let sit until foamy, about 3 minutes. Add flour and salt. Fit stand mixer with dough hook and knead on medium-low speed until dough is shaggy, about 2 minutes.
With mixer running, add softened butter 1 piece at a time until incorporated. Continue to knead until dough is smooth, about 5 minutes. Transfer dough to greased large bowl, cover tightly with plastic wrap, and let rise at room temperature until doubled in size, about 1 1/2 hours.
Grease 12-cup muffin tin. Press down on dough to deflate and transfer to lightly floured counter (do not overflour counter). Divide dough into 2 equal balls (about 1 pound each). Roll one dough ball into 15 by 12-inch rectangle with long side parallel to counter’s edge.
Using pizza wheel, cut dough vertically into 6 (2 1/2-inch-wide by 12-inch-long) strips. Brush tops of 5 strips evenly with 1 tablespoon melted butter, leaving 1 strip unbuttered. Stack strips squarely on top of each other, buttered to unbuttered side, finishing with unbuttered strip on top.
Using sharp knife, cut stacked dough strips crosswise into 6 equal stacks. Place stacks, cut side up, in each of 6 muffin cups. Repeat with remaining dough ball and 1 tablespoon melted butter. Cover tin loosely with plastic and let dough rise at room temperature until doubled in size, 1 1/4 to 1 1/2 hours. Adjust oven rack to upper-middle-position and heat oven to 350 degrees.
Bake until golden brown, 20 to 25 minutes, rotating muffin tin halfway through baking. Brush rolls with remaining 2 tablespoons melted butter. Let cool in muffin tin for 5 minutes. Remove rolls from muffin tin and transfer to wire rack. Serve warm or at room temperature.