Bring a pot of salted water to a boil and cook the linguine until al dente. Drain (do not rinse) and set aside, reserving 3/4 cup of pasta water.
Season the shrimp with salt, black pepper, and Cajun seasoning. Heat 1 tbsp oil in a large non-stick pan over medium heat and cook shrimp for 2 minutes per side until opaque. Transfer to a plate.
In the same pan, add butter and onion; sauté for 3–5 minutes until soft and golden. Add garlic and bell pepper, cooking for another 1–2 minutes until fragrant.
Pour in the heavy cream, scraping up any browned bits from the bottom of the pan. Bring to a gentle boil, then immediately reduce the heat.
Whisk in the Parmesan cheese until melted and the sauce is smooth. Stir in the cooked shrimp, pasta, parsley, chives, and reserved pasta water until everything is well coated and glossy.
Top with extra Parmesan before serving.