Combine first 5 ingredients in a large bowl, stirring well.
Melt 1 1/2 teaspoons butter in a 10-inch ovenproof skillet over medium heat. Pour half of egg mixture into skillet. As mixture begins to cook, gently lift edges of omelet with a spatula, and tilt pan to allow uncooked portions to flow underneath. Cook until browned on bottom. Transfer skillet to oven; broil 5 1/2 inches from heat (with electric oven door partially opened) 1 minute or until top is golden. Cut a 1/4-inch-deep slit down center of omelet. Top omelet with 3/4 cup cheese and 1/4 cup chiles. Loosen omelet with spatula, and carefully fold in half. Slide omelet onto a serving platter, and cut in half.
Repeat procedure with remaining 1 1/2 teaspoons butter, egg mixture, cheese, and chiles. Top each serving with 2 tablespoons salsa just before serving.