Heat oil in a small skillet over medium-high heat. Fry tortillas one at a time until firm, but not crisp. Remove to paper towels to drain grease. Place tortillas in groups of two onto plates, and spread a layer of beans on each group. Top with shredded chicken, cheese, a fried egg, pico de gallo, mozzarella cheese, salsa verde, and avacado. Heat refried beans in the microwave and top with cotija cheese.