To Make Basil Oil:
In 4-quart saucepan on Wolf cooktop over high heat, bring water to a boil. Stir in salt. Carefully add basil leaves to boiling water and blanch for 30 seconds. Using slotted spoon, remove from water and plunge in ice water to stop cooking. Drain and squeeze out as much water as possible from blanched basil leaves. Place in blender or food processor with olive oil and puree for 1 minute on high. Leave oil mixture in bowl for 1 hour to allow the oil to extract as much of the basil flavor as possible. Pour puree mixture in a wire strainer lined with 2 paper coffee filters. Allow to drip for 30 minutes. Very gently wring out basil oil, being careful not to break paper filter. Place oil in small airtight container. Refrigerate until use.
To Assemble Salad:
Slice tomatoes about 1/4” thick. Arrange over a large platter. With a vegetable peeler, shave cheese into thin strips over tomatoes. Drizzle with vinegar. Season with salt and pepper. Stack basil leaves one on top of another and roll into a small rolled bundle, starting with the long end. Slice bundle into thin strips. Sprinkle basil over tomatoes and drizzle 1/8 to 1/4 cup basil oil over all. Serve immediately.
Note: Basil oil may be kept in an airtight container in Sub-Zero refrigerator for up to 2 weeks.