Step 1

Preheat the oven to 300°F.  Line a rimmed baking sheet with aluminum foil and coat it with nonstick cooking spray.  Place the tomatoes on the baking sheet and toss them with 2 tablespoons olive oil (if they are on the vine, just drizzle the tomatoes with the olive oil, and use your hands to make sure they are nicely coated). Season with salt and pepper.  Roast for about 30 minutes, until they are wrinkly and slightly collapsed.

Step 2

Meanwhile, make the basil oil: place the basil, parsley, garlic, lemon juice, 1/2 teaspoon salt and pepper in a food processor, and pulse several times to roughly chop.  With the motor running add 1/2 cup of the olive oil through the top of the processor.  When the oil is added, scrape down the sides of the food processor and process again.

Step 3

Transfer the tomatoes to a serving platter along with any juices that they have released, and let cool to barely warm or room temperature.  They will release some of their juices as they cool, which is not only okay, but desirable.  When ready to serve, cut each burrata in half and nestle the cheese amongst the tomatoes, making sure not to lose any of the creamy filling.  You may want to add a bit more salt and pepper.  Drizzle about half the basil oil over the tomatoes and cheese and serve with the crusty bread, and the rest of the basil oil on the side for extra drizzling.