For the chicken: Preheat your oven to 400 F (If you have an IP, see notes below). In a small bowl or measuring glass, mix the olive oil with chili powder, paprika, cumin, allspice and a generous amount of salt and pepper. Add the chicken chunks to a baking dish and pour the spice/oil mixture over it. Toss the chicken in the mixture. Cover it with foil and bake for 30-35 minutes.
Meanwhile, heat the olive oil in a skillet over medium heat. Add the garlic, green chilies, black beans, corn, chili powder, cumin, oregano, salt and pepper. Mix well and cook for 10 minutes, stirring frequently. Add most of the cheese (save some for the topping), 1/3 cup of salsa verde (2/3 cup if doubling), and half of the chopped cilantro to the mix.
After the chicken is cooked, let it rest for 10 minutes and shred it. Add the chicken to the pan with the veggies and mix well. If the pan isn't big enough, transfer everything to a bowl.
Lower oven temp to 375 F. Prepare a baking dish (I used 9x13) with cooking spray (alternatively, bake right in your containers!). Coat the bottom of your container/s with salsa verde (about 1/4 cup for a large baking dish, or 1-2 TBSP for smaller containers). Scoop the chicken veggie mixture into the fajita tortillas and roll, placing seam side down in the container. Repeat until you're out of tortillas and/or filling. Aim for 2-3 enchiladas per meal.
Pour all the remaining salsa verde on top and spread it around on the tortillas. Add the remaining cheese on top and bake for 20-25 minutes, until cheese is melted and the dish is bubbling slightly. Top with some of the remaining cilantro and garnish with lime wedges. Let the enchiladas cool for about 15 minutes before separating them into containers. That's it!