In a large saucepan, heat 2 tablespoons of the olive oil over medium-high heat. Add the chicken to the pan and season the chicken breast pieces with about 1/2 teaspoon kosher salt or to taste. Sprinkle chicken with 1/4 teaspoon chili powder and 1/4 teaspoon cumin. Cook chicken 5-6 minutes or until cooked through. Remove from the pan and set aside on a plate.
Add the remaining 1 tablespoon of olive oil and add the onion and bell peppers. Sprinkle with remaining 1/4 teaspoon chili powder and 1/4 teaspoon of cumin. Cook veggies over medium-high heat until soft. Remove from the pan and set aside with the chicken.
Add the chicken broth, salsa, and cream to the pan. Add the pasta and cook covered for 15-20 minutes until pasta is done, stirring every so often, replacing the lid quickly so the heat doesn't escape.
When pasta is done, stir in the lime juice and add the chicken and veggies back to the pan heating until warmed through.
Stir in the cheese until melted and top with desired toppings.