Cook fettucine per the package instructions. Reserve 1 cup of the pasta water for later. Drain the pasta and set aside.
Place the uncooked shrimp into a large bowl and add in 2 tablespoons of the pesto. Toss to coat.
Heat 1-2 tablespoons of olive oil in a large skillet over medium heat. Place the shrimp in the skillet and cook for 2-3 minutes on each side, or until the shrimp is pink and cooked through. Transfer the shrimp to a plate and set aside.
To that same skillet, add in the butter, heavy cream, pesto, lemon zest, lemon juice, and the reserved pasta water. Reduce heat to low and let the sauce simmer until it starts to thicken.
Season with salt & pepper to taste and add in the fettuccine noodles and shrimp. Toss to coat and top with fresh basil and lemon zest before serving.