Bring a large pot of salted water to a boil and cook the fettuccine according to package directions; drain, rinse briefly with cold water, and set aside.
While the pasta cooks, drain the jar of roasted peppers. Chop half of the peppers into small pieces and place the remaining peppers and their jar liquid into a food processor or blender; process until smooth.
Heat the olive oil in a large nonstick pan over medium heat. Add the chicken pieces and season lightly with salt and pepper; cook about 5 minutes until cooked through and lightly browned.
Add the finely chopped garlic to the pan and cook about 30 seconds until fragrant, stirring constantly so it does not burn.
Stir in the chopped roasted peppers, the pureed roasted peppers, and the Half & Half (or heavy cream). Reduce heat to medium-low and simmer, stirring occasionally, about 10 minutes until the sauce begins to thicken.
Add the cooked fettuccine and chopped parsley to the pan; toss to coat evenly with the sauce. Adjust seasoning with salt and pepper to taste.
Serve topped with grated Parmesan cheese.