Heat oven to 350°F. In a small pot over medium heat, cook tomato, onion and garlic until tomatoes break down and resembles jam, 15-20 minutes.
Add vinegar and honey; cook until jam thickens, 15 minutes. Add a tbsp. of water if jam get to dry. Season with salt and black pepper; remove from heat. At this point it can be pureed in blender or with an immersion blender for a smoother jam.
On a cookie sheet, arrange bread in a single layer. Top each slice with ¼ cup cheese and 1 slice of prosciutto; bake until cheese melts, 3-5 minutes.
Divide tomato jam among 4 sandwich halves; top with another ¼ cup of cheese remaining sandwich halves. Spread each half with butter.
In a medium skillet over medium heat, cook one sandwich, flipping once, 3-5 minutes per side or until golden. Repeat with remaining sandwiches.