Combine all the ingredients in a small saucepan. Heat over medium heat for 3 to 4 minutes until bubbles form around the basil and garlic. Remove from the heat and let steep for 20 minutes (or 4 hours if time allows). Strain the oil into a bowl or a jar. Discard the basil and garlic.
Cut half of the cherry tomatoes in half, leave the remainder whole (this is more for looks than anything so feel free to halve all of them if you prefer.
Heat 1 tablespoon of the basil oil in a medium frying pan over medium heat. Add the halved and whole tomatoes. Cook for 5 minutes, stirring occasionally, or until the skin blisters and the tomatoes start to soften.
Transfer the tomatoes to a medium bowl. Add 3 tablespoons of basil oil, 1/4 cup of chopped basil, vinegar, shallot, 1/2 teaspoon salt and 1/2 teaspoon pepper; stir to combine.
Wipe the frying pan clean. Pat the salmon dry with a paper towel. Sprinkle the salmon with the remaining salt and pepper. Heat the same pan over medium heat. Add 1 tablespoon of the basil oil to the pan.
Cook the salmon, skin side down for 4 minutes until the skin is crisp. Carefully flip the salmon and cook further for 3 minutes, depending on the thickness of the salmon until the salmon is just cooked.
Serve the salmon topped with the tomato vinaigrette and extra basil leaves. Reserve remaining basil oil in the fridge for another use.