Bring a large pot of salted water to a boil over medium-high heat. Cook the penne pasta according to package directions until al dente (8-10 minutes). Drain the pasta and set aside.
While the noodles are boiling, season cubed chicken with salt, pepper, and paprika.
To a large skillet over medium-high heat, add 1 tablespoon of olive oil. Once hot, add the seasoned chicken cubes and cook for 8-10 minutes, flipping halfway, until golden brown and cooked through. The internal temperature of fully cooked chicken should reach 165°F. Remove the cooked chicken from the skillet, place it on a plate, and tent it with aluminum foil to keep it warm.
To the same skillet, add the remaining 1 tablespoon of olive oil, sliced onions, green bell peppers, and red bell peppers. Cook for 5-6 minutes, or until the onion is softened.
Add the chili powder, cumin, and garlic powder to the skillet with the onions and peppers. Stir until the spices are well combined.
Pour in the chicken broth, heavy cream, diced tomatoes, and diced green chiles. Bring the mixture to a simmer.
Add the cooked chicken and pasta to the skillet and stir to coat it with the sauce. Top with cheese. Remove from heat.
Garnish with fresh cilantro. Serve immediately with lime wedges on the side for squeezing over the dish.