In a small bowl, combine 1 cup ice cubes with 1 cup water. Set it aside.
Bring 2 cups water to a boil in a small saucepan. Add the basil leaves all at once, stirring to make sure they are submerged, and cook for 10 seconds. Immediately transfer them, using a slotted spoon, to the ice bath. Once they have cooled, remove the basil leaves and set them on paper towels. Squeeze the paper towels gently but firmly in your hands to absorb as much liquid as possible.
Pour the oil into a blender, add teaspoon salt and mix on high speed. While the machine is running, add half the basil leaves and process briefly. Then add the remaining basil and puree it (doing this in batches prevents bruising the leaves and keeps the color intact). Transfer the basil oil to a small container, cover and refrigerate for up to 1 week. (If you like, strain the oil through a fine-mesh sieve.)