Combine contents of roll mix box and enclosed yeast packet in a large bowl; stir well. Add warm beer, butter, egg, and 2/3 cup cheese to flour mixture; stir to form a soft dough. Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 5 minutes). Place bowl over dough to cover; let rest 5 minutes.
Shape dough into a ball; place on a baking sheet coated with cooking spray. Let rise in a warm place (85°), free from drafts, 30 minutes or until dough is doubled in bulk.
Preheat oven to 375°.
Bake at 375° for 15 minutes. Sprinkle top of bread with remaining 1/3 cup cheese, and bake an additional 5 minutes. Cool slightly; cut into 12 wedges.