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.
Place the roasted bell peppers from the jar, including the liquid, into a food processor or blender and puree until smooth.
Heat a large non-stick skillet over medium-high heat. Add the butter and melt.
Add the shrimp, paprika, and red pepper flakes to the skillet and cook on high for 3–4 minutes, stirring occasionally, until shrimp are pink and just cooked through.
Add the chopped garlic and sea salt and cook for 1 more minute, then remove the shrimp from the pan and set aside.
Reduce the heat to low and pour the pureed roasted peppers into the same pan. Simmer for about 10 minutes, stirring often.
Stir in the Half & Half and grated Parmesan and cook for 1 more minute until the sauce is warmed and slightly thickened. Turn off the heat.
Return the cooked shrimp to the pan, add the drained fettuccine, and toss gently to combine and coat the pasta with the sauce.
Garnish with chopped parsley and additional grated Parmesan if desired, then serve immediately.