Combine 1 cup all-purpose flour, whole wheat flour, sugar, undissolved yeast and salt in a large bowl. Heat water and oil until very warm (120° to 130°F). Add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add egg and 1/2 cup flour; beat 2 minutes at high speed. Stir in enough remaining all-purpose flour to make soft dough. Cover; let rest 10 minutes.
Roll dough to 1/2-inch thickness. Use 2-inch biscuit cutter to cut dough into circles. Place on lightly greased baking sheet. Cover; let rise in warm, draft-free place until doubled in size, about 40 to 50 minutes. Bake at 375°F for 12 to 15 minutes or until lightly browned. Brush tops with melted butter, if desired.
Recipe Note #1: These rolls freeze well. If planning to freeze, bake for minimum time (do not overbrown). When cool, freeze in airtight container.
To reheat: Place desired number of rolls in pan loosely covered with foil. Heat in 350°F oven for 10 to 15 minutes if thawed, 15 to 20 minutes if frozen.
Recipe Note #2: Rolls are great sliced for “dollar” sandwiches. The dough can also be cut or formed into different sizes and shapes. Example: Use larger biscuit cutter and fold circles of dough in half before baking.