Place chicken strips in a bowl and coat thoroughly with jerk seasoning, lime juice, salt, and pepper. Let the chicken marinate for at least 10 minutes while you prep other ingredients.

Bring a large pot of salted water to a rolling boil. Add penne and cook for 2 minutes less than the package directions indicate. Reserve one cup of starchy pasta water before draining.

Heat olive oil in a large skillet over medium high heat until shimmering. Add chicken strips in a single layer, avoiding overcrowding the pan. Cook for 3 to 4 minutes per side until charred edges develop and the internal temperature reaches 165 degrees Fahrenheit. Remove chicken to a plate and set aside.

Add butter to the same skillet, letting it melt into the flavorful fond left by the chicken. Toss in all the sliced bell peppers and saute for 4 to 5 minutes until slightly softened but still crisp.

Push peppers to the sides of the pan and add minced garlic to the center. Cook for 30 seconds until fragrant, stirring constantly to prevent burning.

Pour in heavy cream and chicken broth, stirring to combine with the garlic and peppers. Add paprika and any remaining jerk seasoning you want for extra heat. Bring the mixture to a gentle simmer and let it reduce for 5 to 6 minutes until thickened enough to coat the back of a spoon.

Add the drained penne directly to the skillet, tossing to coat every piece with sauce. Sprinkle in the parmesan cheese gradually while stirring. If the sauce seems too thick, add reserved pasta water one splash at a time.

Slice the seared chicken into bite sized pieces and add back to the skillet. Gently fold everything together and let it warm through for 2 minutes. Taste and adjust seasoning with salt, pepper, or more jerk seasoning if needed.

Garnish generously with fresh thyme and sliced green onions before serving immediately.