In the bowl of a stand mixer fitted with the paddle attachment, add milk, sugar, egg and egg yolk. Sprinkle the yeast over top and allow it to sit until foamy, about 4-5 minutes.
Add flour and salt, mix until combined, about 2 minutes. Switch to the dough hook and knead on low for 1 minute. Add 8 tablespoons of softened butter, 1 tablespoon at a time. Knead until the dough forms a soft, sticky ball, about 5 minutes.
Place the dough in a large, well-greased bowl. Cover with plastic wrap and allow to rise until doubled, about 1 1/2 hours. Punch dough to deflate, then place onto a lightly floured surface. Divide dough into 2 equal pieces. Using a rolling pin, roll the dough into two rectangles, about 14x16-inches in size.
Using a pizza wheel or pastry wheel, cut each of the rectangles vertically into 6 strips (they should be short or 14 inches in length), for a total of 12 strips. Using a pastry brush, butter the tops of all but two strips (you'll use about 2 tablespoons of the melted butter). Stack 5 strips on top of each other, then place the unbuttered strip on top. Repeat with the remaining strips. Cut each stack into 6 equal squares for a total of 12 stacks.
Place into a well-greased standard size muffin tin, cut side up. Cover with plastic wrap and allow to rise for 1 hour or until doubled in size.
Preheat oven to 350 degrees.
When the rolls have risen, remove plastic wrap and place in the oven to bake for 18-22 minutes or until golden brown on the tops. Remove from the oven and brush with the remaining melted butter. Remove from the pan and serve while warm.