Cut the salmon vertically into 3 or 4 smaller fillets.
Add the oil to a large skillet over medium high heat. Once the pan is hot (you should be able to feel the heat with your hand above the skillet), add the salmon skin side up. Let the salmon cook for 5 minutes on each side. Make sure to leave it undisturbed and do not move it before flipping to get the best sear. Once salmon has cooked on both sides, remove from the pan and set aside.
Add the heavy cream, salt, and pepper and turn the heat down to medium. Let the mixture reach a low boil, stirring frequently (you should see small bubbles), then add in the parmesan cheese and kale.
Cook for a few more minutes, stirring frequently, until the kale cooks down.
Add the salmon fillets back to the hot pan, using a spoon to add sauce on top of them. Ensure the salmon has reached an internal temperature of 145 F (if not, leave on the stove for a few more minutes). Once cooked through, remove the pan from the heat and serve.