In a liquid measuring cup, add lukewarm milk. You can microwave the milk for 30 seconds or you can warm the milk on the stovetop for 1-2 minutes over medium heat.
Sprinkle the yeast over the warm milk and let it sit for 5 minutes.
In the bowl of a stand mixer fitted with the dough hook attachment, add the flours, salt, and honey. Add the yeast mixture, melted butter, and egg to the dry ingredients.
Turn the mixer on low speed and mix for 2-3 minutes and mix until a smooth ball forms and the dough comes cleanly away from the sides of the bowl.
Grease a large bowl with olive oil or spray it with cooking spray. Place dough into the bowl and cover the bowl with plastic wrap. This is the first rise. Place the bowl in a warm place and let the dough rise for 60-90 minutes.
Grease a 9x13 inch baking dish with melted butter. Set that aside.
After the dough has doubled in size, turn the dough onto a lightly floured surface. Pat the dough down so it forms a disk. Cut the dough into equal pieces and form each piece into dough balls.
Place the dough balls into the prepared baking dish. Let the dough rest for the second rise in a warm spot for 60 minutes.
Preheat the oven to 400 degrees. After 60 minutes the rolls should look puffy and light. Brush the tops of the rolls with melted butter and bake for 20-25 minutes or until the rolls are golden brown.