Place the tomato halves in a large bowl and season them with salt, pepper and a splash of red wine vinegar. Toss in most of the torn basil leaves and combine. Set aside.
Rub the salmon fillets all over with a small amount of olive oil and season on both sides with salt and pepper.
Heat a large skillet to medium high. Place the fillets skin side down and cook, undisturbed, for several minutes. You will see the color change on the side of the fillets.
Carefully turn so the skin side is up and finish cooking.
Remove to a plate and hold or, if there's room in the skillet, turn the fillets right side up and move them to the sides.
Stir fry the chorizo for a minute or two to allow the fats to release from the pieces. Toss in the tomatoes and basil. Stir to combine. Cook long enough to warm the tomatoes through.
To serve, arrange the fillets on a plate and spoon the tomatoes, basil and chorizo around. Chop some of the remaining basil leaves and sprinkle over top.