Place all sliced, halved, or tomato wedges in a colander set over a mixing bowl. Season generously with flaky sea salt. Allow to sit. Reserve the tomato liquid for another use, then transfer the seasoned tomatoes to a large platter.
You can leave the burrata balls whole, but we like to cut them into quarters or break them apart with our hands and scatter all around the tomatoes. Season the cheese lightly with flaky sea salt.
Drizzle everything with olive oil and balsamic vinegar. Season with about freshly cracked black pepper, then scatter basil leaves on top (and pistachios, if using). Serve immediately!