COMBINE 1 cup flour, sugar, milk powder, undissolved yeast, salt, black pepper, garlic powder, basil and oregano in a large bowl. Heat water and butter until very warm (120º to 130º F). Gradually add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Stir in onion, peppers and enough remaining flour to make soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover, let rest 10 minutes.
PUNCH dough down; knead in pepperoni, bacon, mushrooms and cheese. Divide dough into 16 equal pieces; shape into balls. Place on greased baking sheets. Cover; let rise in warm, draft-free place until doubled in size, about 45 minutes.
MIX Egg Glaze ingredients with a fork in a small bowl: brush on rolls. Bake at 350ºF for 20 to 25 minutes, or until done. Remove from sheets; serve warm.