Bring a large pot of salted water to a boil. Add linguine or fettuccine, cooking until al dente (8-10 minutes). Reserve 1 cup of pasta water, then drain.

Pat shrimp dry, season with Cajun seasoning. Heat olive oil in a skillet over medium-high heat. Sear shrimp for 1-2 minutes per side until pink. Remove and set aside.

In the same skillet, reduce heat to medium. Add butter, then garlic sautéing until fragrant (about 30 seconds). Stir in tomato paste, deglaze with chicken broth, and simmer for about 5 minutes.

Reduce heat to low, stir in heavy cream and half of the Parmesan cheese until melted and thickened. Adjust consistency with reserved pasta water if necessary.

Combine drained pasta and seared shrimp in the sauce, tossing to coat. Stir in remaining Parmesan and parsley. Adjust seasoning with salt and pepper to taste.

Plate immediately, garnishing with fresh parsley and a sprinkle of Parmesan. Serve warm.