In a small bowl, combine the first 7 ingredients. In a 10-inch ovenproof skillet, melt the butter over medium heat and add the tortilla pieces. When tortilla is soft, pour eggs into the skillet and cook 3 to 5 minutes, lifting eggs to allow the uncooked portion to flow underneath. Remove from heat; sprinkle egg evenly with cheese and place skillet in a 325 degrees F oven for 3 to 4 minutes or until the cheese melts. Spread avocado mixture on top 1/2 omelet and return it to the oven for 5 to 7 minutes. Fold the omelet in half to serve.