Start by bringing a large pot of salted water to a boil. Add the fettuccine and cook according to package instructions until al dente. Once done, reserve about 1 cup of pasta water, then drain and set aside.
In a large skillet, heat 1 tablespoon of olive oil and 1 tablespoon of butter over medium-high heat. Once the butter has melted, add the shrimp, 3 minced garlic cloves, red pepper flakes, salt, and pepper. Cook for about 2-3 minutes until the shrimp turns pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of olive oil and 2 tablespoons of butter. Add the remaining minced garlic and sauté for about 30 seconds until fragrant. Sprinkle the flour over the garlic and stir to combine, cooking for another minute.
Slowly whisk in the chicken broth, ensuring there are no lumps. Once combined, pour in the heavy cream and continue to whisk until the sauce is smooth. Let it simmer for about 3-4 minutes until it thickens slightly.
Stir in the prepared pesto, lemon zest, and lemon juice. Mix well, and let the sauce simmer for another minute. Taste and adjust seasoning if necessary.
Add the cooked fettuccine and shrimp back into the skillet, tossing to coat everything evenly in the creamy sauce. If the sauce is too thick, add a bit of the reserved pasta water until you reach your desired consistency.
Remove from heat and stir in the grated Parmesan cheese. Serve immediately, garnished with extra Parmesan and fresh parsley.
