Prepare the roasted pepper sauce. In a blender or food processor, combine the roasted red peppers, 2 cloves of minced garlic, and a pinch of salt. Blend until completely smooth, about 1 minute. Set aside.
Bring a large pot of water to a boil and salt it generously (it should taste like seawater). Add the fettuccine and cook until al dente according to package directions, usually 9-11 minutes.
While pasta cooks, prepare the shrimp. Pat the shrimp dry with paper towels and season with salt and pepper. This ensures they’ll sear rather than steam when they hit the pan.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the shrimp in a single layer (work in batches if needed) and cook for 1-2 minutes per side until just pink and opaque. Remove to a plate and set aside.
In the same skillet, add the remaining tablespoon of oil and reduce heat to medium. Add the shallot and remaining garlic, cooking until fragrant and translucent, about 1 minute. Be careful not to burn the garlic!
Pour in the roasted pepper puree and stir to combine. Simmer for 2-3 minutes to meld the flavors.
Stir in the heavy cream and red pepper flakes (if using). Allow the sauce to gently simmer for 2-3 minutes until slightly thickened.
Reserve 1 cup of pasta cooking water before draining the fettuccine. This starchy water is key for creating a silky sauce that clings to the pasta.
Add the cooked pasta directly to the sauce, tossing to coat evenly. If the sauce seems too thick, add some of the reserved pasta water, a little at a time.
Gently fold in the cooked shrimp, Parmesan cheese, and lemon juice. Continue tossing until everything is well coated and the shrimp is warmed through.
Taste and adjust seasoning with salt and pepper as needed.
Remove from heat and stir in the fresh basil. Serve immediately with additional Parmesan cheese for sprinkling.