Place the shrimp in a large bowl. Add the Cajun seasoning and 2 tablespoons of olive oil. Toss until evenly coated, then season lightly with kosher salt.
Heat 2 tablespoons olive oil in a large, deep skillet over medium-high heat.
Working in batches if necessary, arrange the shrimp in a single layer. Cook for approximately 1 minute per side, or until browned and cooked through. Transfer the shrimp to a clean plate and set aside.
Carefully wipe out the skillet.
Place the onion, red bell pepper, and garlic in a food processor. Pulse for about 1 minute, scraping down the sides as necessary, until a smooth vegetable puree forms.
Heat the remaining 2 tablespoons olive oil in the same skillet over medium heat.
Add the onion and pepper puree. Cook for 7–10 minutes, stirring frequently, until much of the moisture has evaporated and the mixture becomes thicker. Add a small splash of water if it begins browning too quickly.
Pour in the heavy cream and stir well, scraping up any flavorful browned bits from the bottom of the skillet.
Bring the mixture just to a gentle boil, then remove the skillet from the heat.
Gradually whisk in the finely grated Parmesan until the sauce becomes smooth and creamy.
Return the cooked shrimp to the skillet and gently stir until coated in the Cajun cream sauce.
Stir in the parsley and chives.
Divide the warm cooked rice among serving bowls or plates. Spoon the Creamy Cajun Shrimp and Rice mixture generously over the top.
Finish with additional Parmesan and fresh herbs, if desired, and serve warm.