Grease a 9x13-inch metal baking pan; set aside.
In a small saucepan, stir milk, honey, and 4 tablespoons butter together. Heat over low heat just until butter melts and honey dissolves. Cool to about 100-105 F.
Pour the milk mixture into the bowl of a stand mixer.
Add the yeast and warm water. Let stand for 5-10 minutes, or until yeast is foamy.
Add the whole wheat flour and 1/2 cup all-purpose flour and salt to yeast mixture. Using a dough hook, mix on low speed for about 1 minute.
With the mixer still going, add remaining all-purpose flour, 1/4 cup at a time. You may not need to use all of the flour.
Mix about 1 ½ minutes, or until dough starts to clear the sides of the bowl.
Knead on low speed for about 2 more minutes, or until dough is smooth and elastic – the dough will still be slightly sticky to the touch.
Place dough in a greased bowl, turning it to grease the top. Cover the dough with a clean, dry dish towel.
Let it rise in a warm place, free from draft, for about 15 minutes.
Turn the dough onto a lightly floured surface, and divide into 15 equal pieces.
Form each piece into a ball and place on the prepared baking sheet.
Cover the baking sheet with the dish towel, and let the dough rise for about 15 minutes.
Bake at 375ºF for about 12 minutes, or until the rolls are golden brown.
Toward the end of the baking time, melt remaining 2 tablespoons butter. Set aside.
Optional, brush rolls with melted butter.