Preheat oven to 375 degrees F.
Brown the potatoes. Into a large skillet over medium-high heat, add vegetable oil. When the oil is hot, add the potatoes. Cook, stirring frequently, for 3 minutes until lightly browned.
Cook the aromatics. Add the onions, salt, and black pepper. Continue cooking for 2 minutes. Add the garlic and continue cooking for an additional 1 minute.
Add the beans and chiles. Stir in the black beans and green chiles, allowing the mixture to heat through, about 3 minutes. Remove from heat.
Stir in the cheese. Add 1/2 cup cheese, stirring to combine.
Fill the tortillas. Into each tortilla, add 1/3 cup of the filling then roll and place seam side down in a prepared 9×13-inch baking dish.
Add the sauce. Pour enchilada sauce evenly over the top of the enchiladas.
Top with more cheese. Sprinkle with any additional filling and the remaining 1 cup of cheese.
Bake it. Bake, uncovered, for 30 minutes then serve.