Preheat oven to 275F. Toss halved tomatoes with olive oil, minced garlic, oregano, salt, and pepper. Arrange cut-side up on a baking sheet.
Roast for 2 hours until visibly shrunken, jammy, and slightly caramelized at the edges.
Toast the bread until golden and crisp. Rub with the whole garlic clove while still hot.
Tear the burrata into large pieces and distribute over the toast.
Spoon the warm roasted tomatoes over the burrata. Drizzle with olive oil and balsamic glaze, add basil and flaky salt.
Serve immediately while warm.