Cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add the sliced jerk chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced onion and bell peppers. Sauté for about 3-4 minutes until they are tender. Add the minced garlic and cook for an additional 1 minute.
Pour in the chicken broth and heavy cream, stirring to combine. Add the dried thyme, paprika, salt, and pepper. Bring the mixture to a simmer.
Add the cooked penne pasta and jerk chicken back into the skillet. Toss everything together until well combined and heated through, about 2-3 minutes.
Serve hot, garnished with fresh parsley.