Start by placing the chicken breasts between two pieces of plastic wrap. Use a meat mallet to gently pound them to an even thickness, about 1 inch. This ensures they cook evenly. Season the chicken with garlic powder, chili powder, salt, and pepper on both sides.
Lightly dredge each seasoned chicken breast in flour, shaking off any excess. This step will give your chicken a lovely, golden crust when cooked.
In a large skillet, heat the butter and olive oil over medium heat until the butter has melted and the mixture is hot.
Add the dredged chicken breasts to the skillet. Cook for about 5-7 minutes on each side or until the chicken is golden brown and cooked through. The internal temperature should reach 165°F. Once done, remove the chicken from the skillet and set aside.
In the same skillet, add the chicken broth and salsa, stirring to combine and scrape up any flavorful bits stuck to the pan. Bring the mixture to a simmer.
Return the cooked chicken to the skillet, spooning some of the salsa sauce over the top. Sprinkle the shredded Mexican cheese evenly over the chicken. Cover the skillet and let it cook for an additional 2-3 minutes, or until the cheese is melted and bubbly.
Once the cheese is melted, remove the skillet from the heat. Garnish with freshly chopped cilantro if desired. Serve hot over rice, with tortillas, or alongside a fresh salad.