Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente. Drain, rinse with cold water, and set aside.
While the pasta cooks, reserve about half of the jarred roasted peppers and chop them into small pieces.
Place the remaining jarred roasted peppers with their liquid into a food processor or blender and process until smooth.
Heat the olive oil in a large non-stick skillet over medium heat. Add the chicken pieces, season with salt and pepper, and cook about 5 minutes until lightly browned and cooked through.
Add the finely chopped garlic to the skillet and cook about 30 seconds, stirring, until fragrant.
Pour the blended roasted peppers and the Half & Half (or heavy cream) into the skillet with the chicken. Stir to combine.
Cook the sauce, stirring occasionally, for about 10 minutes until it starts to thicken.
Add the cooked fettuccine and chopped roasted peppers to the skillet and toss with the sauce until evenly coated. Stir in the chopped parsley and adjust seasoning with salt and pepper if needed.
Serve immediately and sprinkle with grated Parmesan cheese.
