OK, full disclosure: I did not come up with this recipe all on my own. It's the creation of the talented chef Didier Mantarou, and I had the privilege of trying it first-hand at his restaurant Miel Brassiere in Boston. I thought of this recipe when I went to develop one with olive oil because it's the exact kind of recipe where the role of olive oil, and the quality of it, is important to the dish. You'll see that this is so much more than a tomato and mozzarella dish (the burrata could've told you that), and it's incredibly easy to prepare.
In a medium-sized sauté pan, combine the yellow cherry tomatoes, 1 cup of the red cherry tomatoes, and 2 tablespoons of the oil. Place over low heat. Season with salt and pepper, to taste, and cook until the cherry tomatoes are soft, for 1-2 minutes. Remove the tomato mixture from the pan and add the remaining oil and red cherry tomatoes. Sauté lightly with a little bit of basil. Cook until the tomatoes become very soft, for 5-10 minutes, then add to a blender to purée until smooth.
In a small saucepan, reduce the red wine over high heat until it has a rich, thick consistency, about 15 minutes. To assemble the dish, pour the tomato purée into the bottom of a bowl. Place 1/2 of a burrata piece on the purée, drizzle with the red-wine reduction, add a dash of pesto, and garnish with fresh basil.