Preheat 2 cast iron pans over high heat.
Lay bread slices side by side and drizzle with olive oil and vinegar. Top one piece of bread with a slice of mozzarella, tomato slices, prosciutto, basil, and remaining slice of mozzarella.
Close sandwich and spread half the butter on top slice. Place sandwich, buttered side down, onto one pan and quickly spread remaining butter over top of sandwich. Using a hot pad or kitchen towel, place second pan on top of sandwich and press gently. Reduce heat to low and cook, continuing to press, until sandwich is golden brown and cheese has melted, about 4 minutes. Serve immediately.