Step 1: Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper.
Step 2: Prepare your heirloom tomatoes. Thoroughly wash your 2 lbs of mixed heirloom tomatoes and then core them. For larger tomatoes, cut them into 1-inch thick wedges. Smaller ones can be halved.
Step 3: Arrange the tomatoes on the prepared baking sheet in a single layer, ensuring they are not overcrowded.
Step 4: Drizzle the tomatoes generously with 3 tablespoons of extra virgin olive oil.
Step 5: Scatter 2 thinly sliced cloves of garlic over the tomatoes.
Step 6: Sprinkle 1 teaspoon of dried oregano evenly over the tomatoes.
Step 7: Season generously with salt and freshly ground black pepper to taste.
Step 8: Roast in the preheated oven for 25-30 minutes, or until the tomatoes are tender, slightly collapsed, and their edges are beginning to caramelize.
Step 9: While the tomatoes are still warm from the oven, arrange the torn 8 oz fresh burrata cheese pieces artfully among them on the baking sheet or transfer to a serving platter. The warmth of the tomatoes will gently soften the burrata.
Step 10: Garnish with 1/4 cup of fresh basil leaves, torn or chopped.
Step 11: Drizzle 2 tablespoons of balsamic glaze over the entire dish.
Step 12: Serve immediately, perhaps with some crusty bread for dipping into the delicious juices.