Prep Time: 15 minutes
Cook Time: 20 minutes
Bring salmon to room temperature and sprinkle both sides with kosher salt.
In a skillet set over medium-high heat, add 2 tablespoons of neutral oil. When hot and shimmery, add the salmon, skin-side down, and cook for about 3 minutes, working in batches if needed. Turn the heat down to medium and cook for an additional 1 to 2 minutes. During this time, the skin will get crispy and lift off the pan; do not move the salmon at all.
Flip the salmon and cook on the opposite side for an additional 3 minutes. Transfer the salmon to a plate to rest.
Meanwhile, make the sauce: Add the butter to the same pan set over medium heat. When the butter has melted, add the lemon juice, diced anchovy, Italian parsley, tomatoes, and green olives. Cook until the tomatoes have softened and butter has thickened, about 5 minutes. Pour the sauce and the cherry tomato mixture over the salmon and serve.
Notes On Styling
When plating it all up, place the salmon in the center of the dish and carefully drizzle the sauce over top for bonus presentation points (use a dish with a bit of a lip to hold in all that saucy goodness); an extra sprinkle of chopped parsley wouldn’t hurt, either.