Bring a large pot of salted water to a boil. Add the fettuccine or linguine and cook according to package instructions until al dente, typically 8-10 minutes. Drain the pasta, reserving about 1/2 cup of pasta water, and set aside.
In a medium mixing bowl, add the large shrimp and sprinkle the Cajun seasoning over them. Toss well to ensure each shrimp is coated evenly with the spice blend.
Heat the olive oil in a large skillet over medium heat. Once hot, add the seasoned shrimp in a single layer. Cook for approximately 2-3 minutes per side until the shrimp are pink and opaque. Once cooked, transfer the shrimp to a plate and cover to keep warm.
In the same skillet, add the diced onion. Sauté for 3-4 minutes until the onion is translucent and softened. Then, add the minced garlic and sauté for an additional minute until fragrant and golden.
Slowly pour in the chicken broth, using a wooden spoon to scrape up any browned bits from the bottom of the skillet—this adds flavor. Stir in the heavy cream and bring the mixture to a gentle simmer over low heat, allowing it to thicken slightly.
Add the halved cherry tomatoes and fresh spinach to the skillet. Cook for 2-3 minutes, or until the spinach has wilted and the tomatoes have softened. Introduce the drained pasta and cooked shrimp back into the skillet. Toss everything together gently, cooking on low heat. If the sauce seems too thick, gradually add the reserved pasta water until the desired consistency is reached. Season with salt and pepper according to your taste.
Plate the creamy Cajun shrimp pasta generously and finish with a sprinkling of grated Parmesan cheese on top. Garnish with freshly chopped parsley for a pop of color. Dive in and enjoy the delightful flavors!