All ingredients ready? Let's begin!
Remove the salmon from the refrigerator 20 minutes prior to cooking.
Pat dry with paper towels and set aside on a platter.
In a large skillet over medium-high heat, warm the olive oil.
Season both sides of the salmon fillets with the salt and pepper.
Add the fillets, skin side up, to the hot oil, and cook until golden brown for about 4 minutes. The flesh should start to become opaque along the base.
Turn the fish over and continue to sauté until the skin is crisp, approximately 2 more minutes. The fillets do not have to be cooked all the way through at this point. Transfer them to a plate.
Turn the heat down to medium. Add the butter to the pan. As soon as it melts, add the garlic and cook until aromatic, approximately 1 minute.
Deglaze the pan with white wine, stirring until it just starts to reduce. You want to scrape up and incorporate any salmon skin bits. These are tasty.
Add the tomato halves to the pan and season with a little salt and pepper. Cook until the tomato skins blister and the juices are released.
Add the spinach, stir well, and cook just until the spinach wilts but is still deep green.
Whisk or stir in the heavy cream and bring the sauce to a low simmer. Once simmering, reduce the heat to low and stir in the parmesan and 3 tablespoons of the basil.
Simmer until slightly thickened, about 3 minutes.
Place the salmon fillets in the pan, skin side down. Spoon some sauce over the fillets and continue to simmer until the salmon is just cooked through, approximately 2 to 3 minutes. The flesh should be pink and just a little firm.
Transfer the salmon to a large serving bowl or individual plates and spoon the sauce over the fish. Garnish with the remaining tablespoon of the basil. Serve immediately.