Pour cherry tomatoes onto a baking sheet or oven-proof dish. Drizzle with olive oil, sprinkle with salt and pepper, and top with oregano. Roast for 15-20 minutes or until the tomatoes begin to blister and char. Remove from oven and set to the side.
Place the roasted tomatoes on a large tray. Open the burrata and cut it into smaller pieces, nestling the cheese around the tomatoes.