Preheat a grill over medium flame or an oven to 350°F.
In a medium bowl, combine the tomatoes, shallot, olives, olive oil, salt and pepper. Add more oil if you find the mixture to be dry. Taste and check the seasoning.
Slice the bread crosswise into ½-inch slices. Toast the bread on the grill or in the preheated oven for 5-10 minutes. Once the bread is toasted to your liking, remove from the heat and rub with the peeled garlic.
Top with a smothering of burrata and then spoon the tomato mixture over top, making sure to drizzle some of the oil from the mixture as well. Finish with fresh basil leaves to garnish. Serve immediately.