Grease bottom and sides of a very large mixing bowl, set aside for later.
Add warmed milk to bowl of a stand mixer fitted with the dough hook. Add yeast and sugar, then stir and let sit for 5 minutes. Mixture should be frothy/foamy.
Add honey, egg, egg yolk, melted butter, salt and 3 cups of flour. Mix on LOW speed for a minute or two, then add remaining 1/2 cup flour. Mix on LOW for another minute, until it all combines.
Dough should be soft and thick, and slightly sticky. You're looking for the dough to pull away from the sides of the bowl as it mixes.
Increase mixer speed to MED to "knead" the dough for a minute or two. The dough will slap against the sides of the bowl when finished.
Turn dough out into prepared mixing bowl, turning dough to coat all sides. Cover with plastic wrap and a kitchen towel, then place in a warm spot to rise for about 2 hours, until dough has doubled in size.
When dough has doubled in size, punch the dough down (this removes air bubbles), then turn dough out onto a lightly floured surface (I use my countertop).
Cut dough into fourths, then cut each fourth into 4 equal sized pieces, for a total of 16 pieces of dough.
Form into balls and place into a buttered 9x13 baking dish. Cover with plastic wrap and let rise until doubled and puffy in appearance, about 45 minutes to an hour.
Preheat oven to 350 F degrees. Bake dinner rolls for 18-22 minutes, or until golden brown and the tops of rolls have a hollow sound when tapped.