In a bowl, toss the chicken pieces with the spices until they are well-coated. Heat 1 tbsp of olive oil in a large, high-walled skillet over medium-high heat. Add the chicken and cook until they are cooked through and no longer pink, about 5-7 minutes. Remove the chicken to a plate or bowl and set aside.
Heat the remaining 1 tbsp of olive oil in the skillet and add the chopped bell peppers and onions. Cook until the veggies are soft and starting to slightly brown, about 3-4 minutes.
Add the garlic and cook until fragrant, about 1 minute. Remove the veggies to the same plate as the chicken.
Add the chicken broth, salsa, heavy cream, and penne pasta to the skillet and stir. Bring to a boil and then lower heat to medium-low so it is at a gentle simmer. Cover with a lid and cook until the pasta is al dente, about 9-10 minutes.
When the pasta is cooked, remove the lid, and add the chicken and veggies back to the skillet. Cook the chicken and veggies with the sauce and pasta for a few minutes.
Add the shredded cheese and stir until melted. Add the cilantro (or parsley) and stir. Remove from heat and serve while hot.