1. Preheat oven to 350 degrees Fahrenheit (180 degrees Celsius).
2. Place the eggs in a medium-sized bowl and beat well. Add cheese, salt, and pepper.
3. Heat oil in a frying pan over medium flame. Sauté onions in oil until golden brown. For broccoli quiche, add onions and broccoli to egg mixture and mix well. For red pepper or mushroom quiche, add red peppers or mushrooms to the frying pan with the onions and sauté another five minutes. Combine vegetables with egg mixture.
4. Pour mixture into greased muffin tins, filling three quarters of the way. Bake for 30 minutes, until golden and puffy.
For variations, two red peppers, diced, or half a pound (225 grams) fresh or 8 ounces (225 grams) canned mushrooms can be used instead of the broccoli.