Pat the salmon fillets dry with paper towels. Season generously with Cajun seasoning on both sides.
Heat the olive oil in a large skillet over medium-high heat. Once hot, add the salmon fillets and sear for 4-5 minutes on each side, or until cooked through and flaky. Remove the salmon from the skillet and set aside.
In the same skillet, melt the butter over medium heat. Add the chopped green onions and cook for 1-2 minutes, until softened. Pour in the heavy cream and lemon juice, stirring to combine. Simmer for another 2-3 minutes, until the sauce has slightly thickened.
Return the salmon fillets to the skillet and spoon the New Orleans sauce over the top. Let it simmer for another minute or two, allowing the salmon to soak up the flavors.
Serve immediately, garnished with extra green onions, if desired. Enjoy!