Preheat the oven to 375°F.

Heat the olive oil in a large oven-safe skillet over medium heat. Add the drained Hatch diced green chiles and cook for 1–2 minutes, stirring occasionally. Stir in the green enchilada sauce and black beans. Bring the mixture to a gentle simmer and cook for about 10 minutes, stirring occasionally and smashing some of the beans. Taste and season with salt and pepper as desired.

Use the back of a spoon to make four small wells in the sauce mixture. Carefully crack one egg into each well. Sprinkle the shredded Monterey Jack cheese evenly over the sauce, avoiding the egg yolks if you want them to remain visible. Transfer the skillet to the oven and bake for about 10 minutes, or until the egg whites are set and the yolks reach your preferred doneness. For firmer yolks, bake a few minutes longer. Remove the skillet from the oven and let it rest for 2 minutes. Serve hot, topped with sliced avocado.