Heat 1 tablespoon olive oil and the butter in a large skillet or braiser over medium-high heat.
Add the chicken pieces, sprinkle with the Tex Mex seasoning, and cook 4–6 minutes, stirring, until the chicken is browned on all sides.
Add the remaining 1 tablespoon olive oil, chopped onion and chopped bell peppers to the skillet and cook 3–4 minutes until softened.
Stir in the minced garlic and cook about 30 seconds until fragrant.
Add the diced fire-roasted tomatoes (with juices), drained black beans, corn, chili powder, cumin, chicken broth, and long-grain rice; stir to combine and bring to a boil.
Cover the skillet, reduce heat to low, and simmer 20–25 minutes, stirring once halfway through, until the rice has absorbed the liquid and is tender.
Remove from heat and gently stir in 1 cup of the shredded Monterey Jack cheese.
Sprinkle the remaining 1/2 cup cheese over the top, cover and let sit 3 minutes until the cheese melts.
Garnish with chopped cilantro and serve with lime wedges.