Toss the shrimp with Cajun seasoning, 2 tablespoons olive oil, and a pinch of salt until evenly coated.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat.
Cook the shrimp in batches for about 1 minute per side until lightly browned and cooked through. Transfer to a plate.
Wipe the skillet clean.
In a food processor, blend the onion, bell pepper, and garlic until a smooth puree forms.
Bring a large pot of salted water to a boil and cook the linguine until al dente. Reserve 1 cup of pasta water before draining.
Heat the remaining olive oil in the same skillet over medium heat.
Cook the vegetable puree for 7–10 minutes, stirring frequently, until thickened and most of the liquid has evaporated.
Pour in the heavy cream and bring to a gentle simmer.
Remove from the heat and whisk in the Parmesan until smooth and creamy.
Add the cooked shrimp, drained linguine, parsley, chives, and about ¾ cup reserved pasta water.
Toss everything together until the Creamy Cajun Shrimp Pasta is coated in a silky, glossy sauce. Add more pasta water if needed.
Serve immediately with extra Parmesan and fresh herbs.