Add olive oil and onion to the bottom of an 8x8 baking dish. Add tomatoes, cut side up, in an even layer over the onion; season with salt and pepper, to taste.
Place into oven and roast until slightly tender, about 20 minutes. Add garlic in an even layer over the tomatoes. Place into oven and roast until the tomatoes are soft, an additional 10 minutes; let cool 10-15 minutes.
Combine tomatoes, bread, Parmesan and broth in blender or food processor until smooth.
Serve immediately, garnished with burrata, balsamic reduction and basil leaves.