Get a pot of salted water boiling and set aside covered until ready to cook pasta
Butterfly the chicken breasts and pound them to 1/4" thick
Season each chicken breast all over with 1/2 tsp salt, 1/2 tsp pepper, and 1 tbsp jerk seasoning
Thinly slice the peppers. Thinly slice the scallions, separating the whites and greens. Mince the garlic
Cook pasta until just al dente. Reserve 0.5 cup of pasta water for later
Pan fry the chicken breasts in a tbsp of oil over medium-high heat (or grill), getting the first side lightly charred, about 3-5 minutes. Cook on the second side for another 2-3 minutes until cooked through and temping 160 F. Reserve chicken on a plate, letting it rest for at least 3 minutes, then chop into bite sized pieces
Deglaze the pan with water to loosen any charring, and wipe out the pan
Heat a tablespoon of oil over medium-low heat and add peppers and scallion whites. Cook for 3-4 minutes until softened
Add garlic and remaining 2 tablespoons of jerk seasoning and cook until fragrant, about 30 seconds
Add heavy cream, reserved pasta water, and any accumulated chicken juices to pan, stirring frequently until thickened, about 2-3 minutes. If including peas add them now
Add pasta to the pan, tossing until well coated
Turn off heat, and add 0.5 cup of parmesan
Divide pasta between bowls, topping with remaining 0.25 cups of parmesan, scallion greens, and grilled chicken or shrimp