Heat Big Jim's Red Chile Sauce over low heat. While it is heating through, heat the oil in a frying pan. Using tongs, dip each tortilla in the hot oil just long enough to soften it. DO NOT FRY! Place tortillas, one at a time, on oven-proof plate, spoon on one or two tablespoons of red chile sauce, sprinkle with cheese and onion, and repeat the process with two more tortillas. Put plate in a warm oven to melt cheese and repeat the procedure until all four plates are in oven.
Melt butter in a frying pan and fry eggs the way you like them (over-easy works best for this dish). Place one egg on top of each enchilada plate. Decorate edges of plate with shredded lettuce and serve.
Combine 1 cup of broth with the flour in a medium-sized saucepan. Add the remaining broth and cook on medium heat until thickened. Stir the chicken, chile, and garlic salt into a broth and set aside. Heat 1/2-inch of shortening in a heavy pan at medium-high heat. Quickly dip each tortilla into the shortening to soften. Drain on absorbent towels. Combine 1 cup cheese, onion, and sour cream in a medium-size mixing bowl.
Assemble the enchiladas by placing 1/4 cup of sauce on each dinner plate, followed by a tortilla, 1/4 cup of sauce, and 1/3 cup of sour cream mixture. Top with remaining sauce and cheese. Place in oven heated at 350 degrees for 45 minutes, or until cheese melts.