Marinate chicken chunks with jerk dry rub seasoning in a bowl, then seal in a ziplock bag and refrigerate for at least 3 hours or overnight.
Bring a pot of salted water to boil and cook pasta according to package instructions until al dente, about 6-8 minutes.
Heat olive oil in a medium skillet over medium-high heat. Sear the marinated chicken chunks for 3-4 minutes on each side until cooked through. Remove and set aside.
In the same skillet, sauté chopped bell peppers, minced garlic, and scotch bonnet pepper until fragrant and slightly softened, about 1-2 minutes.
Add smoked paprika, jerk seasoning, and flour. Stir to combine and cook briefly.
Whisk in heavy cream, chicken stock, and white cooking wine. Cook while stirring until sauce thickens and smoothens.
Return the seared chicken to the skillet and add thyme sprigs. Reduce heat to low and simmer for 15-18 minutes until sauce thickens and chicken and peppers are tender.
Stir in grated parmesan cheese until melted and sauce becomes creamier.
Add cooked pasta to the skillet and stir well to coat evenly with sauce.
Remove thyme sprigs. Serve immediately garnished with chopped scallions or extra parmesan if desired.