Bring a large pot of water to a boil. Add a tablespoon of oil and cook the pasta according to the package instructions. Drain the cooked pasta and set aside.
In a bowl, mix the chicken pieces with the jerk seasoning and 1 tablespoon of olive oil. Let it marinate for at least 30 minutes. Heat a skillet over medium heat and cook the chicken thoroughly until it's no longer pink, about 7-8 minutes.
In the same skillet, add another tablespoon of olive oil and sauté the red and orange bell peppers along with the garlic for about 2-3 minutes or until they start to soften. Add the fresh thyme, cooked chicken pieces and a tablespoon of jerk seasoning. Stir well.
Pour the heavy cream into the skillet and let it simmer for 1-2 minutes until it thickens slightly. Add the grated parmesan cheese and stir it in until fully incorporated. Taste and adjust the seasonings by adding salt and pepper as needed.
Add the cooked pasta to the skillet and mix well, ensuring the pasta is evenly coated with the sauce. Cook for another 2-3 minutes on medium heat until the dish is heated through.
Transfer the Jamaican Rasta Pasta to plates or a serving dish. If desired, garnish with chopped green onions or scallions for an extra burst of flavor and color.