In a blender, combine basil, oil, vinegar, and 1 tablespoon water. Blend until smooth, 2 to 3 minutes. Season vinaigrette with salt and pepper.
With dental floss or a warm knife (wiped clean after each slice), thinly slice cheese. Arrange tomatoes and goat cheese on a serving plate; drizzle with dressing to taste. Serve garnished with basil leaves.