Heat ½ cup oil in a large skillet over medium-high heat until shimmering. Add one tortilla at a time, flipping once, until lightly brown and crisp.
Drain the freshly fried tortilla on a paper towel-lined baking sheet. Repeat this process until all tortillas are fried, adding more oil if needed.
In another skillet, heat the enchilada sauce.
While enchilada sauce is heating up, make beans by combining refried beans, shortening, and milk in a pot over medium heat. Stir vigorously with a fork or wire whisk until silky smooth. Add cheese and let melt before serving.
Using the same frying pan where you fried tortillas, fry the eggs to your preference (runny, well done).
Transfer two tortillas side by side onto a plate. Add some refried beans and spread it over tortillas.
Add some enchilada sauce (a large spoonful) and spread over the beans.
Place your fried eggs on tortillas and then finish with more sauce on top, avocado, crema, cilantro, and queso fresco.