Combine warm milk and sugar in a large mixing bowl. Add yeast and let sit while the yeast dissolves, about 5 minutes.
Add egg, egg yolk, and flours to the yeast mixture and mix with a dough hook on low or by hand until dough begins to form, 1 – 3 minutes, then add salt and mix briefly.
Increase speed to medium and begin to add soft butter one piece at a time or work into dough by hand one piece at a time, until incorporated. Continue to mix or knead until the dough is smooth and pulls away from the side of the bowl, about 10 – 15 minutes.
Transfer dough to a clean bowl, coat lightly with oil, and cover. Let rise in warm place until doubled in size, about 45 minutes.
Brush a standard 12-serving muffin tin with melted butter and set aside; reserve melted butter. Place dough on a lightly floured surface and divide into three equal pieces. Roll each piece into an 18-inch long rope. Divide each rope into 12 equal pieces and cover with a towel. Shape each piece into a small, smooth ball.* Place three balls, seam side down, into each muffin cup. Cover and let rise in a warm place until doubled in size, about 20 minutes. Meanwhile, preheat oven to 375°F.
Brush rolls with melted butter and bake until golden-brown, about 15 minutes, rotating pan halfway through baking. When rolls have baked, immediately brush with remaining melted butter and cool in pan for 5 minutes. Serve warm.
