Rinse the salmon fillets, dab dry and place them in a large coated pan with the skin side facing upwards. Place on the stove at medium to high heat. When the pan gets hot and the salmon begins to fry (after about 3 minutes), turn it over and fry it from the skin side for about 5 minutes until the skin is super crispy and the salmon is just cooked (depending on the thickness of the fillets). Season to taste.
Meanwhile, wash the cherry tomatoes, cut them in half and mix them in a bowl with most of the plucked basil leaves and 1 tablespoon of red wine vinegar as well as a pinch of sea salt and pepper. Crush and stone the olives. Finely chop the pulp and mix with 1 tsp olive oil and 1 dash of water.
Cut the chorizo into thin slices and put them in the pan for the last 2 minutes or so to make the salmon. Then add the tomatoes and cook for about 30 seconds. Arrange on plates, with the salmon on top, spread the chopped olives on top and garnish with the remaining plucked basil leaves.