Prepare the chicken by mixing jerk seasoning, 1 tablespoon of olive oil, garlic powder, and smoked paprika in a medium bowl. Add the chicken, coat it with the mixture, and cover the bowl with plastic wrap. Let the chicken marinate in the refrigerator for 2 hours to 24 hours. Remove the chicken from the fridge about 1 hour before cooking to bring it to room temperature. Preheat the oven to 400 degrees. Heat the remaining 1 tablespoon of olive oil in a cast-iron skillet over medium heat. Sear the chicken in the skillet, browning it on both sides, which should take about 3 minutes per side.
Once the chicken is seared, transfer the skillet to the oven and roast the chicken until its internal temperature reaches 165 degrees Fahrenheit, which should take approximately 15 to 20 minutes. Then, transfer the chicken to a cutting board, let it rest for about 10 minutes, and slice it at an angle.
While the chicken is roasting, prepare the pasta by bringing a pot of well-salted water to a boil over high heat. Cook the pasta following the package instructions, then drain it and set it aside.
In a heavy pot set over medium heat, add 2 tablespoons of oil and sauté the bell peppers and green onions until the peppers are slightly softened, which should take about 4 minutes. Add the minced garlic and cook until it becomes fragrant, approximately 1 more minute.
Add the 1/4 cup of jerk seasoning to the pot and mix well. Add the thyme and the pierced pepper. Pour in the heavy cream and vegetable stock, and bring the mixture to a simmer. Stir in the Parmesan cheese, then add the cooked pasta. Top the dish with the jerk chicken and garnish it with additional green onions. Serve the dish hot.