Pat the shrimp thoroughly dry with paper towels. This is important because dry shrimp will sear rather than steam. Place them in a bowl and add the Cajun seasoning, smoked paprika, garlic powder and black pepper. Toss until every shrimp is lightly coated.
Heat the olive oil and butter in a large skillet over medium-high heat. Once the skillet is hot, arrange the shrimp in a single layer. Cook for approximately 1–2 minutes on the first side, until golden and lightly charred around the edges. Flip and cook for another 1–2 minutes, just until the shrimp are opaque and cooked through. Don’t overcook them. Add the lime juice, toss briefly and transfer the shrimp to a plate.
Reduce the heat to medium. In the same skillet, add 1 tablespoon butter. Add the diced onion and cook for 3–4 minutes, stirring occasionally, until softened. Add the garlic and cook for about 30 seconds, just until fragrant.
Add the uncooked rice directly to the skillet. Stir for approximately 1 minute, coating the grains in the butter and aromatics. This gives the finished rice more flavor and helps preserve some texture.
Pour in the chicken broth. Add the corn, Cajun seasoning, salt and black pepper. Stir well and bring to a gentle boil. Reduce the heat to low and cover the skillet. Cook for approximately 15–18 minutes, or according to the cooking time of your rice, until the rice is tender and most of the broth has been absorbed. Avoid stirring repeatedly while the rice cooks.
Once the rice is tender, reduce the heat to low. Stir in the heavy cream and Parmesan. Cook uncovered for another 2–3 minutes, stirring gently, until creamy. The finished rice should be creamy but not soupy or mashed. If it’s too thick, add a small splash of chicken broth. If it’s too loose, simmer uncovered for another minute or two.
Arrange the cooked Cajun shrimp over the creamy corn rice. Don’t stir them completely into the rice — keeping them on top makes the dish much more appealing and prevents the shrimp from overcooking. Warm everything together for about 1 minute.
Sprinkle with chopped green onions and parsley or cilantro. Add freshly cracked black pepper and lime wedges. Serve immediately with an extra squeeze of fresh lime juice.