Brush both sides of bread with oil, then pat cheese evenly onto both sides.
Heat a dry nonstick skillet over medium. Add coated bread and cook, flipping once, until cheese is golden brown and melted, about 5 minutes.
Place one tomato slice on a plate. Sprinkle with vinegar, then drizzle with oil; season with salt and pepper. Layer with toast and remaining tomato slice. Sprinkle with vinegar, then drizzle with oil; season with salt and pepper. Top with basil and serve.
