Bring a large pot of well-salted water to a boil. Cook the linguine or fettuccine until al dente according to the package directions, usually 8 to 12 minutes. Reserve 1/2 cup pasta water, then drain.

Pat the shrimp dry, then toss them with 1 tablespoon Cajun seasoning and 1/4 teaspoon freshly ground black pepper. Dry shrimp brown more readily and hold onto the seasoning.

Heat the olive oil in a large skillet over medium-high heat. Add the shrimp and cook for about 1 to 2 minutes per side, just until pink and opaque, then transfer them to a plate.

Reduce the skillet heat to medium and add the butter, onion, and bell pepper. Cook for 4 to 5 minutes, stirring occasionally, until the vegetables soften.

Add the minced garlic, remaining Cajun seasoning, and optional red pepper flakes. Stir constantly for about 30 seconds, just until the garlic is fragrant.

Pour in the heavy cream and chicken or seafood broth. Simmer gently for 3 to 5 minutes, stirring occasionally, and avoid an aggressive boil so the cream stays smooth.

Stir in the finely grated Parmesan and cook for 1 to 2 minutes, until the sauce thickens slightly. If needed, add reserved pasta water one tablespoon at a time to loosen the sauce.

Add the drained pasta and cooked shrimp to the skillet. Toss until every strand is coated and the shrimp is heated through, then taste before adding salt because Cajun seasoning and Parmesan may already be salty.

Garnish with chopped fresh parsley and serve immediately. Offer lemon wedges at the table for a bright finish.