With a serrated knife, cut the tomatoes into ¼″ thick slices. Arrange them on a large serving platter, overlapping their edges and varying the shapes as best you can.
Cut the burrata or mozzarella into ¼″ to ½″ slices (burrata is tricky since the inside is so creamy; I cut it into ½″ slices and gently tugged the slices into smaller sections, see photos). Tuck the cheese around and underneath the tomatoes, dispersing it relatively evenly across the platter.
Sprinkle basil leaves all over, and tuck a few more into the crevices. Drizzle the olive oil over the salad. Sprinkle generously with salt and pepper.
For the best flavor (if you have the time), let the salad rest for 30 minutes so the tomatoes release some juices and the flavors have time to mingle. This salad is best served within a few hours. Leftovers will keep, covered and refrigerated, for up to 3 days
MAKE IT DAIRY FREE/VEGAN: As long as you’re using great tomatoes, you’ll enjoy this salad without cheese. If you’d like some creaminess, I think this salad would be nice with dollops of my vegan sour cream or with slices of avocado.
CHANGE IT UP: Try substituting ripe peaches for some of the tomatoes!