1. Preheat broiler.
2. Combine first 3 ingredients in a small bowl, stirring with a whisk.
3. Place 1 cheese slice on top of each muffin half. Place muffin halves on a baking sheet. Broil 1 minute or until cheese melts.
4. Heat a small nonstick skillet over medium heat. Add oil to pan; swirl to coat. Add egg mixture to pan; cook without stirring until mixture sets on bottom. Draw a spatula across bottom of pan to form curds. Continue drawing spatula across bottom of pan until egg mixture is slightly thick, but still moist; do not stir constantly. Remove from pan immediately and place on muffin bottom.
5. Spread ketchup over cheese on muffin top. Sprinkle egg with hot sauce, if desired, and cover with muffin top. Serve immediately.