Bring a large pot of salted water to a rolling boil. Add the fettuccine and cook according to package instructions until al dente, usually around 8-10 minutes. Once cooked, carefully drain the pasta, making sure to reserve 1 cup of the pasta water for later use. Set the pasta aside.
In a mixing bowl, combine the shrimp with the Cajun seasoning. Toss gently but thoroughly until all the shrimp are evenly coated in the spices.
Heat the olive oil in a large skillet over medium-high heat. Once hot, add the seasoned shrimp to the skillet in a single layer. Sauté the shrimp for about 2-3 minutes on each side, or until they are cooked through and turn a lovely pink color with an opaque finish. Remove the shrimp from the skillet and place them on a plate; set aside.
In the same skillet, add the minced garlic and sauté for approximately 30 seconds, or until fragrant. Be careful not to burn the garlic. Next, pour in the heavy cream and allow it to come to a gentle simmer.
Gradually stir in the grated Parmesan cheese, whisking until it melts completely and the sauce becomes creamy and smooth. Add the chopped sun-dried tomatoes and mix well. If your sauce appears too thick, slowly incorporate the reserved pasta water, a little at a time, until the sauce reaches your desired creamy consistency.
Add the cooked fettuccine and the sautéed shrimp back into the sauce. Gently toss everything together until the pasta is thoroughly coated and heated through. Taste and adjust seasoning with salt and pepper as needed.
Once combined, remove the skillet from heat. Sprinkle the dish with freshly chopped parsley for a pop of color and flavor. Serve immediately, accompanied by lemon wedges on the side for a zesty finish that enhances the dish.