Besides Karen lovely recipe (I am copying it too) maybe you are referring to something like this:

Southwestern Breakfast Quesadilla
This recipe is courtesy of The Inn at Cascade, Cascade, CO

1 4-ounce can of green chiles
1 green onion diced
1 tablespoon butter
6 large eggs
1/4 cup milk
1/4 teaspoon cumin
Salt and pepper to taste
4 ounces Pepper (Monterey) Jack Cheese
2 large flour tortillas
Salsa
Sour Cream

Saute green onion and green chiles in butter in a large omelet pan.

Beat eggs with milk, cumin, salt and pepper. Pour egg mixture over onion and green chile, scramble slightly.

In an electric skillet at 325 degrees melt a little butter and layer 1 flour tortilla with 1/2 cheese, cooked scrambled eggs remaining cheese and top with 2nd flour tortilla.

Cook and flip once until both sides are golden brown and cheese is melted. Slice into four quarters and top with salsa and a dollop of sour cream.