Begin by cooking the fettuccine pasta according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
In a bowl, toss the shrimp with Cajun seasoning, ensuring they are evenly coated.
In a large skillet, heat 2 tablespoons of olive oil over medium-high heat. Add the seasoned shrimp and cook for 2-3 minutes on each side, or until they turn pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet, reduce the heat to medium and add the remaining tablespoon of olive oil. Add the minced garlic and sauté for about 1 minute until fragrant.
Pour in the heavy cream, bringing it to a gentle simmer. Stir in the grated Parmesan cheese until melted and creamy. If the sauce is too thick, gradually add in the reserved pasta water to reach your desired consistency.
Return the cooked shrimp to the skillet, mixing them into the creamy sauce. Add the cooked fettuccine, tossing everything together gently until well combined.
Season with salt and pepper to taste, if needed. Stir in the chopped parsley for freshness.
Serve immediately, garnished with lemon wedges for an added zest.