Heat a large skillet over medium high heat. When the pan is hot, add 1/4 cup butter. Once the butter is almost melted, add onion. Saute onion in butter until just starting to soften. About 5 minutes. Add garlic and stir until fragrant.
Stir in flour. Stir for about two minutes or until flour and butter are combined and starting to turn a slightly darker color. Add heated milk and whisk constantly until the gravy thickens.
Add green chles, salt and pepper. Remove sauce from heat and set aside.
In a bowl, whisk the eggs until mixed well. Heat another large skillet over medium heat. Add the remaining 2 tablespoons of butter and when butter has melted, add eggs and scramble until just starting to set up. Set aside.
In a small bowl, mash avocados.
To build the burritos, Heat the stack o 6 burritos in the microwave for 30 seconds. This will make them pliable and easy to roll. Spoon 2 tablespoons of gravy, 1/6 of the eggs and 1/6 of the avocado on each tortilla.
Roll up and place seam side down in a 6 1/2 by 10 inch baking dish.
Spoon remaining gravy over tortillas. Sprinkle with cheese. Bake at 350 degrees 15 - 20 minutes or until hot. Top with chopped tomatoes, sliced jalapeno, cilantro and sour cream if you'd like. Serve with salsa, optional.
Add more milk to gravy, if needed, to thin consistency. This recipe makes a good amount of gravy. You may not need to use all of it.