For vinaigrette:
Blend all ingredients in blender until basil is very finely chopped and vinaigrette is thick; season to taste with salt and pepper. (Can be made 6 hours ahead. Cover and chill.)

For salad:
Cut small skin-deep X on end opposite stem of each tomato. Drop tomatoes into saucepan of boiling water; cook 30 seconds. Using slotted spoon, transfer tomatoes to plate. Starting at X, peel skin off tomatoes. Cut 1/3 to 1/2 inch off end opposite stem of each tomato. Using small spoon, scoop out insides of tomatoes, leaving shells intact. Mix cubed mozzarella cheese and chopped basil in medium bowl. Divide cheese mixture among tomato shells, packing gently. (Can be made 2 hours ahead. Cover tomatoes and chill. Bring to room temperature before continuing.)

Invert 1 filled tomato on each plate. Pour vinaigrette into 6 shot glasses. Place 1 shot glass next to each tomato. Garnish each tomato with basil leaf.

Notes

A basil vinaigrette is served in a shot glass alongside each tomato; guests can drizzle it on to taste.

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