It's a new form of cheese to me: Burrata. It's a gooey variant of Mozzarella (a cheese which I do not like, even Buffalo Mozzarella. Flavorless and rubbery). Burrata, like Mozzarella, is a fresh cheese.
I'd be willing to try Burrata with sliced tomato. They may have it at our gourmet Italian market, and I am told Whole Foods carries it sometimes. I hate Whole Foods on principle, but they have always had a fine cheese department. Me love cheeses with fruits, nuts, jellies for dessert.
A good tomato platter might be sliced tomatoes, sliced mango or peach, a chunk of oozing burrata, a handful of chopped fresh basil, and a balsamic dressing.