Bring a large pot of salted water to a boil. Add the linguine and cook according to package instructions until al dente, usually about 8–10 minutes. Drain the pasta, reserving about 1/2 cup of the pasta water, and set aside.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Toss the peeled and deveined shrimp with the Cajun seasoning until evenly coated. Add the shrimp to the hot skillet in a single layer and cook for about 2 minutes on each side until they turn pink and develop a slight char. Remove the shrimp from the pan and set aside.
In the same skillet, add the diced onion, minced garlic, and bell pepper. Sauté for 3–4 minutes until the vegetables soften and become fragrant. Scrape up any bits left from the shrimp to incorporate that flavor.
Pour in the heavy cream and chicken broth, stirring to combine. Let the mixture simmer gently for 3–5 minutes until it thickens slightly. Stir in the grated Parmesan cheese until melted and smooth. Season the sauce with salt and pepper to taste. If the sauce is too thick, add a splash of the reserved pasta water to loosen it.
Add the cooked linguine and shrimp back into the skillet with the sauce. Toss everything together over low heat until the pasta is well coated and the shrimp are warmed through.
Remove the skillet from heat. Sprinkle chopped parsley over the top for a fresh burst of color and flavor. Serve immediately with extra Parmesan on the side if desired.