Heat the oven to 400°F.

• Peel and coarsely chop the yellow onion.
• Rinse the black beans and pinto beans.

In a large frying pan over medium-high heat, warm 2 to 3 teaspoons oil until hot but not smoking. Add the onion, Southwestern spice blend, and tomato paste, season with salt and pepper, and cook, stirring occasionally, until the onion starts to soften, 2 to 3 minutes. Add the beans, green chiles, tomatoes, and ¾ cup water and cook, stirring occasionally, until slightly thickened, 3 to 5 minutes. Transfer the sauce to a medium bowl and season to taste with salt and pepper. Wipe out the pan.
While the sauce cooks, heat the tortillas.

• Remove 12 tortillas from the package; save the rest for another use.

Lay a damp kitchen towel on a sheet pan. Arrange the tortillas on one end of the towel, overlapping them slightly; cover them with the other end of the towel. Heat in the oven until warmed through and just pliable, 4 to 5 minutes. Remove from the oven and let stand, still covered, until ready to use. Be careful of the hot towel when unwrapping.

On a work surface, lay the tortillas side by side. Spoon about ½ cup enchilada sauce and 1 tablespoon Mexican cheese blend across the center of each tortilla. Carefully roll up the tortillas and place them, seam side down, in a large baking dish. Top the enchiladas with the remaining sauce and cheese. Bake until the enchiladas are heated through and the cheese is melted, 5 to 7 minutes.
While the enchiladas cook, prepare the garnish and the eggs.

• Coarsely chop the cilantro.

In the same pan used for the enchilada sauce, warm 1 to 2 teaspoons butter or oil over medium heat until hot but not smoking. Crack the eggs directly into the pan and season with salt and pepper. Cook until the whites have set and the yolks are slightly runny, 2 to 3 minutes. If you prefer firmer yolks, cook for 1 to 2 minutes longer.

Transfer the enchiladas to individual plates and top with the eggs. Sprinkle with the cilantro and serve.