Dissolve the yeast in a glass measuring cup with the warm milk.
In the bowl of a stand mixer fitted with a hook attachment, combine the egg, egg yolk, 1/2 cup melted butter, honey, salt, yeast mixture and 2 cups of bread flour.
Beat on your mixer’s lowest speed for a minute, then increase to a medium speed and mix until a smooth yet sticky dough forms. Begin to gradually add the remaining flour (you may not need the full 1-1/2 cups) until a soft dough forms that pulls away cleanly from the sides of the bowl.
Turn the finished dough out onto a floured surface (or try kneading with a stand mixer). Knead until smooth and elastic, about 6-8 minutes. Then transfer it to a lightly greased bowl, turning it over once to grease the top. Cover and let rise in a warm place until doubled in size, about 1 hour and 15 minutes.
Punch down the dough and turn it out onto a lightly floured work surface. Divide and shape into 24 equal-sized balls. Arrange the balls in greased 8×8-inch baking pans (12 rolls per pan) and cover them with clean kitchen towels.
Let rise, undisturbed, in a warm place until doubled in size, about 1 hour. The time is entirely dependent on room temperature. You can place in the oven to rise . Place a pan of hot water in the bottom of oven. Turn light on oven and place dough on oven rack. Once risen remove from the oven.
Preheat oven to 350F. Bake until golden brown, about 20-25 minutes. Remove promptly and immediately brush the tops of each roll with the remaining 2 tablespoons of melted butter.