Cook pasta in boiling water until al dente or desired tenderness.
Slice raw chicken (about finger size). Toss the chicken with 1 Tablespoon jerk seasoning. In a dutch oven, fry the chicken in 1 Tablespoon oil until cooked (for about 5 minutes, until no pink left). Remove the chicken from the dutch oven and set it aside.
Use the same dutch oven to cook the bell peppers with 1 Tablespoon oil for 5 minutes. Add garlic and jerk seasoning and cook for another minute.
Pour in the chicken broth and bring to a boil, then add coconut milk and reduce heat to a simmer. Heat until the broth mixture thickens (about 5 minutes).
Add the chicken and parmesan cheese.
Remove from heat and stir well.
Once the cheese is melted, stir in the penne. As the pasta cools a bit, sauce will begin to thicken and stick to the pasta, keep gently mixing until all the ingredients are incorporated well.
Serve with reserved ½ cup of parmesan cheese.