Add shrimp to a medium bowl and toss with 1 tablespoon Cajun seasoning, 1 tablespoon lime juice, and 4 minced garlic cloves. Set aside.
Bring a large pot of water to a boil. Add a small handful of salt and pasta. Cook until al dente, about 8-12 minutes. Reserve 1/2 cup pasta water before draining. Set aside.
While the pasta cooks, heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add onions and bell peppers, 1/2 teaspoon salt, and 1/4 teaspoon pepper and cook until peppers reach desired crisp-tenderness, approximately 5 minutes. Remove to a plate.
To the same skillet (don’t wipe it out), melt 1 tablespoon butter and one tablespoon olive oil over medium-high heat. Add shrimp mixture and cook 3-4 minutes, just until shrimp are opaque and cooked through. Scrape shrimp and garlic/juices into a bowl. Set aside. After shrimp is cool enough to handle, you can chop tails off if you desire.
To the same skillet (don’t wipe out), melt 1 tablespoon butter with 1 tablespoon olive oil. Sprinkle in flour and 1-3 teaspoons Cajun seasoning (3 teaspoons for more heat), and optional cayenne pepper (if you want it spicy) and cook, while stirring, for 2 minutes, then turn heat to low. Slowly whisk in chicken broth and heavy cream, stirring constantly until smooth. Stir in diced tomatoes.
Turn heat to medium-high and bring the sauce to a simmer. Simmer until thickened, stirring occasionally, approximately 3-5 minutes.
Reduce heat to low and stir in lime juice followed by Parmesan cheese until melted. Stir in the cooked shrimp, vegetables, and pasta until well coated in sauce, adding additional reserved pasta water or heavy cream if needed to reach desired consistency. Taste and season with additional salt, pepper and/or cayenne pepper to taste.
Garnish with freshly grated Parmesan cheese, fresh parsley, and lime juice (optional).
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Notes
I find 2 tablespoons Cajun seasoning and 1/4 teaspoon cayenne pepper to be on the spicy side as you would expect from a Cajun pasta.If you are sensitive to heat or want to make the dish very kid-friendly then use 1 tablespoon Cajun seasoning with the shrimp and only 1 teaspoon Cajun seasoning with the roux and omit the cayenne pepper.
At the end of cooking if you want more heat you can always add more, but you can’t take it away.