Preheat oven to 400°F (200°C). Toss the halved tomatoes with olive oil, salt, black pepper, and oregano. Spread on a baking sheet and roast for 15-20 minutes, until soft and slightly caramelized.
Heat a grill pan or skillet over medium heat. Brush both sides of the bread slices with olive oil. Toast for 2-3 minutes per side until golden brown and crisp. While still warm, rub each slice with the cut side of a garlic clove for extra flavor.
In a small blender or mortar and pestle, blend the basil leaves, olive oil, lemon juice, and salt until smooth.
Place the toasted bread on a plate. Tear the burrata and spread it evenly over each toast. Top with roasted tomatoes. Drizzle with the basil mixture and balsamic glaze (if using). Sprinkle with flaky sea salt and freshly cracked black pepper.