Heat the olive oil in a skillet over MEDIUM-LOW heat. Add the onions and sauté for 3 minutes, or until tender. Add the garlic, chicken, beans, corn, cumin, salt, and pepper. Sauté for about 2 minutes then add the salsa verde. Increase heat to MEDIUM and cook until bubbly, then lower the heat and allow to simmer for 3 or 4 minutes. Remove from the heat, stir in the cilantro, and set aside to rest.
Preheat oven to 425 degrees F with the oven rack in the top third of the oven (one level up from center). Line a large rimmed baking sheet with parchment paper and set it aside.
Wrap 6 tortillas in a double layer of wet paper towels. Microwave for 50 seconds, or until warm and pliable.
Remove one tortilla from the paper towels and place it on a cutting board or other work surface (keep remaining tortillas wrapped in the wet paper towels). Brush one side of the tortilla with vegetable oil and flip it over. Place about 2 tablespoons of shredded cheese on one half of the dry side of the tortilla, then place about ¼ cup of the chicken mixture on top of the cheese. Fold the tortilla in half and place it on the prepared baking sheet, pressing the top down lightly. Repeat with remaining warm tortillas and filling. Then, repeat the process by heating the remaining 6 tortillas, brushing with oil, and stuffing.
Bake in the preheated oven for about 20 minutes or until tortillas are golden and crispy. If the tops of the tortillas begin to curl as they bake, open the oven and press down very lightly on the taco with a spatula (be careful not to squish the filling out). Remove from the oven and let them rest for about 5 minutes.
Use a spatula to transfer tacos to a platter, if desired. Garnish the tacos with your toppings of choice. Tortillas will continue to crisp as the tacos rest so it’s best to garnish them before they crisp up too much (the top should be easy to lift after they rest 5 minutes).