Cook the pasta: Bring a large pot of salted water to a boil.
Cook the pasta until just al dente. Reserve 1 cup of pasta water, then drain and set aside.
Season the shrimp: Pat the shrimp dry. Toss with 1 tablespoon of Cajun seasoning, a pinch of salt, and a little black pepper.
Sear the shrimp: Heat 1 tablespoon butter and the olive oil in a large skillet over medium-high heat.
Add the shrimp in a single layer and cook 1–2 minutes per side until pink and just opaque. Transfer to a plate. Do not overcook.
Sauté aromatics: Reduce heat to medium.
Add remaining 2 tablespoons butter. Stir in garlic and cook 30 seconds until fragrant. Add tomato paste and cook 1 minute to deepen flavor.
Build the base: Stir in crushed tomatoes and broth.
Simmer 2–3 minutes to marry the flavors. Whisk in remaining Cajun seasoning (adjust to taste).
Make it creamy: Lower heat. Add heavy cream and cream cheese.
Whisk until smooth and lightly thickened, 2–3 minutes. If it gets too thick, loosen with a splash of broth.
Finish the sauce: Stir in Parmesan and lemon zest. Add a squeeze of lemon juice to brighten.
Taste and season with salt, pepper, and red pepper flakes if you want extra heat.
Toss with pasta: Add the cooked pasta to the skillet. Toss, adding reserved pasta water a little at a time until the sauce is glossy and coats the noodles.
Return the shrimp: Fold the shrimp back into the pan just to warm through, 1 minute. Don’t let it simmer or the shrimp will toughen.
Garnish and serve: Sprinkle with chopped parsley or chives.
Top with extra Parmesan and a final crack of black pepper. Serve hot.