Dice the onion, mince the garlic, drain and rinse the beans, and shred the Monterey Jack or cheddar if you bought a block. Heat the oil in a 4-quart / 3.8 L saucepan over medium heat, add the onion and cook for 4 minutes until soft. Stir in the garlic, chili powder, cumin and salt and cook for 30 seconds until fragrant.
Pour in the enchilada sauce and salsa and stir. Nestle the chicken breasts into the sauce, bring to a gentle simmer, cover and cook for 20 minutes, flipping once at the 10-minute mark, until an instant-read thermometer reads 165 F / 74 C in the thickest part. While the chicken simmers, heat the oven to 190 C / 375 F.
Move the chicken to a cutting board. Simmer the sauce uncovered for 3 minutes until it coats the back of a spoon, then spoon 1/2 cup (120 ml) of it into a 23 x 33 cm / 9 x 13-inch baking dish and spread it flat. Shred the chicken with two forks and stir it back into the rest of the sauce.
Wrap the tortillas in a damp paper towel and microwave for 45 seconds so they bend without cracking. Lay 6 tortillas in the dish, overlapping them and tearing the last ones to fill gaps. Top with half the chicken, half the beans, half the corn and one-third of the shredded Monterey Jack or cheddar. Repeat with the remaining tortillas, chicken, beans and corn, then scatter the last of the cheese over the top.
Cover the dish with foil and bake for 15 minutes. Remove the foil and bake 10 minutes more, until the cheese is bubbling with browned spots at the edges.
Rest the bake for 10 minutes so the layers set. Cut into 6 squares and top each with about 3 tbsp of Greek yogurt, chopped cilantro and a lime wedge.