Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add chicken pieces and cook until browned on all sides, about 5 minutes. Remove chicken and set aside.
Add sliced Andouille sausage to the same pot and cook until browned, about 3 minutes. Remove sausage and set aside with the chicken.
Add diced green bell pepper, red bell pepper, and onion to the pot. Cook, stirring occasionally, until vegetables are softened, about 5 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Stir in diced tomatoes with juice, Cajun seasoning, smoked paprika, dried thyme, dried oregano, and cayenne pepper. Cook for 2 minutes to combine flavors.
Pour in chicken broth and bring to a boil.
Add uncooked penne pasta to the boiling broth. Reduce heat to medium-low and simmer uncovered, stirring occasionally, until pasta is almost tender, about 12 minutes.
Return the cooked chicken and sausage to the pot. Stir in frozen peas and cook for an additional 3 minutes until peas are heated through and pasta is fully cooked.
Season with salt and freshly ground black pepper to taste.
Remove from heat and garnish with chopped fresh parsley before serving.