Remove the burrata from the fridge. If your tomatoes were refrigerated, let them sit at room temperature as well.
Prepare the breadcrumbs: Pulse a small piece of bread in a food processor until you have crumbs with some small chunks. Heat 1 Tbl olive oil in a pan over medium heat, add the breadcrumbs, and toast until golden, stirring often. Transfer to a bowl and mix in garlic powder, parmesan, and salt and pepper. Return briefly to the pan and cook for 1–2 minutes, stirring until fragrant, then let cool in the bowl.
Thinly slice tomatoes (about ¼ inch / ¾ cm) and arrange them on a serving plate.
Tear the burrata into small clusters and scatter over the tomatoes. Spoon dollops of green olive pesto evenly across the dish. Sprinkle breadcrumbs on top if serving immediately, or serve them on the side to keep crisp.
To finish, drizzle the dish with olive oil, season with salt and pepper, and add fresh basil. Serve and enjoy!