Press a wonton wrapper into the bottom of each section of a greased muffin pan.
In a mixing bowl, combine the onion, bell pepper and ham cubes. Stir to combine.
Place a large spoonful of the filling mixture into each of the cups in the muffin pan.
Beat together 6 eggs, and mix in ¼ cup of heavy whipping cream. Add salt and pepper to taste.
Pour some of the egg mixture into each of the cups. If you overfill over the top of the wonton wrapper, it is not that big of a deal because the egg will harden and form the shape of the muffin tin cup as it cooks.
Bake for 12-15 minutes until cooked through.
Sprinkle some shredded cheddar cheese onto the top of each of the omelette cups. Garnish with fresh herbs if desired, and serve immediately.