Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente; drain, rinse briefly with cold water, and set aside.
While the pasta cooks, chop half of the roasted peppers into small pieces and transfer to a bowl.
Place the remaining roasted peppers and their jar liquid into a food processor or blender and process until smooth; set aside.
Heat the olive oil in a large nonstick skillet over medium heat. Add the chicken pieces, season with salt and pepper, and cook about 5 minutes until cooked through and no longer pink.
Add the chopped garlic to the pan and cook about 30 seconds until fragrant.
Stir in both the chopped and the pureed roasted peppers, then add the Half & Half (or heavy cream). Bring to a simmer and cook, stirring occasionally, about 10 minutes until the sauce thickens slightly.
Add the cooked fettuccine and chopped parsley to the skillet; toss to combine and heat through. Adjust seasoning with salt and pepper.
Serve topped with grated Parmesan cheese.