Preheat the oven to 400°F.
Add the cherry tomatoes, smashed garlic, olive oil, kosher salt, black pepper, and crushed red pepper flakes (if using) to a small baking dish. Toss until evenly coated.
Nestle the lemon halves cut side down among the tomatoes.
Roast for 25 minutes, or until the tomatoes are blistered and softened and the garlic is tender.
Remove the baking dish from the oven. Squeeze the roasted lemon over the tomatoes, then lightly smash the tomatoes with the back of a spoon or fork, allowing the juices to combine with the roasted garlic and olive oil.
Increase the oven temperature to 450°F. Return the baking dish to the oven and roast for an additional 10–15 minutes, until the tomatoes are bubbling and beginning to caramelize and the garlic is lightly browned.
Remove from the oven and immediately top with the burrata and fresh basil.
Finish with flaky sea salt and a little extra olive oil, if desired.
Serve warm with thick slices of grilled sourdough or crusty bread for scooping up every last drop of the roasted tomato juices.