Pour each salsa into its own small pan and let it simmer. Taste for salt and heat. If too thick, add a splash of water; if too sharp, simmer 2 extra minutes.
Dry-skillet or direct gas flame for 15–30 seconds per side. Keep them wrapped in a towel so they stay soft.
Spread warm refried beans or pile a handful of chips between where the eggs will go. You want a divider.
Medium skillet, a slick of oil or butter. Crack two eggs, cook until whites set and yolks still jiggly. Salt and pepper—don't skip.
Tortilla down, egg on top of each. Spoon roja over one egg, verde over the other. Keep the sauces mostly on their sides (let them flirt, not elope).
Crumble queso, shower with cilantro, add onion, avocado slices, and a squeeze of lime. Serve hot. Stare proudly.