Heat olive oil in a large, deep skillet over medium-high heat, then add the sliced bell peppers and onion, cooking for 5 minutes until they begin to soften.
Add the minced garlic and jerk seasoning, stirring for 1 minute until fragrant.
Pour in the chicken broth and heavy cream, then add the penne pasta, thyme, salt, and pepper, stirring to combine.
Bring the mixture to a boil, then reduce heat to medium-low and simmer uncovered for 15-18 minutes, stirring frequently, until the pasta is al dente and the sauce has thickened.
Stir in the Parmesan cheese until melted and creamy.
Garnish with fresh parsley and serve immediately.