Combine whole wheat flour, undissolved yeast, sugar, and salt in a large bowl. Heat milk, water, and butter until very warm (120ºF to 130ºF). Add to flour mixture.
Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add ¼ cup all-purpose flour; beat 2 minutes at high speed. Stir in enough remaining all-purpose flour to make a soft dough, up to 1 ¼ cup flour. Knead using the dough hook attachment or on a lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover and let rest 10 minutes.
Divide dough into 12 equal pieces; shape into balls. Place in greased 8 or 9-inch round pan.
Cover rolls lightly with foil or a kitchen towel. Let rise in a warm draft-free area until doubled in size, about 30 minutes. Brush tops with egg wash.
Bake at 375ºF oven for 15 to 20 minutes or until done. Brush with melted butter if desired and serve warm.