Put 4 heavy dinner plates in oven and preheat to 200°. Heat salsa in a small saucepan over low heat, covered.
Fill a large frying pan with 1/2 in. oil and heat over medium heat until the handle of a wooden spoon bubbles when you stand it in the oil. Remove plates from oven. Using tongs, fry each tortilla 2 seconds per side. Drain against side of pan, then overlap 2 tortillas on each warm plate. Pop in oven to keep warm.
Reduce heat to medium low. Cook 4 eggs, gently spooning oil over yolks to set them, 2 minutes for firm whites and runny yolks.
Spoon about 3 tbsp. warm salsa onto each plate of tortillas. Using a slotted spatula or spoon, transfer 2 eggs to each plate, draining against side of pan first, and top with another 3 tbsp. salsa. Keep warm in oven while frying and plating remaining 4 eggs. (You may have to increase the heat a little for the second batch.)
Sprinkle eggs with jack cheese, then green onions, cotija, and oregano. Spoon beans alongside and top with jack cheese.
*If you can spend more time cooking, check out our recipes for Salsa Ranchera, Chorizo Refried Beans, and Mexican Red Rice.
Note: Nutritional analysis is per serving.