Preheat a large 12-inch deep skillet on low-medium heat and swirl oil to coat the bottom of the pan.
Add the onion, garlic, and bell peppers. Sauté for 3 minutes, stirring occasionally, until the vegetables are slightly softened.
Push the vegetables to the side of the skillet, leaving space to add the diced chicken. Sprinkle the chicken with 1 teaspoon cumin, salt, and black pepper.
Cook the chicken for about 5 minutes, stirring occasionally, until it's lightly browned.
Add the corn, black beans, diced tomatoes (with the liquid), zucchini, taco seasoning, and the remaining cumin. Stir everything to combine.
Cover the skillet and let the mixture cook on low-medium heat for 10 minutes, stirring once halfway through.
Once the vegetables are tender but not overly soft, sprinkle the shredded cheese over the top of the skillet. Cover and cook for 2-3 more minutes until the cheese melts.
Remove from heat and garnish with chopped green onions and cilantro before serving.