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 to stop cooking, and set aside.
Place the roasted bell peppers and the jar liquid into a food processor or blender and puree until completely smooth.
Heat a large nonstick skillet over medium-high heat. Add the butter, then add the shrimp, paprika, and red pepper flakes. Cook shrimp 3–4 minutes, stirring, until pink and just cooked through.
Add the chopped garlic and sea salt to the shrimp and cook 1 more minute. Remove the shrimp from the pan and set aside.
Reduce heat to low and add the pureed roasted peppers to the same skillet. Simmer, stirring often, for about 10 minutes to meld flavors.
Stir in the Half & Half and grated Parmesan and cook 1 minute more, then turn off the heat.
Return the cooked shrimp to the skillet, add the drained fettuccine, and toss gently until the pasta is evenly coated with the sauce.
Garnish with chopped parsley and extra Parmesan if desired, then serve immediately.