Heat oil over medium to medium-low heat. Cover the bottom of a non-stick, oven safe skillet with the chile verde sauce and heat until lightly bubbling.
Make 3-5 shallow wells in the sauce and gently crack an egg into each well (amount of eggs will depend on how large your skillet is). The egg should not be touching the bottom of the skillet.
Sprinkle with cotija cheese (or queso fresco), cover skillet, and cook slowly over low heat until the egg yolks are to your liking. For me it was just under 8 minutes on the stovetop. Alternatively put covered skillet in 325 degree oven for 5 minutes or until yolks are cooked to your liking.
Serve with additional sauce, black beans, cilantro, extra cheese or straight out of the pan!