Whisk together the champagne vinegar, white balsamic vinegar and a pinch of kosher salt. Stream the olive oil into the vinegar mixture, whisking; set aside.
Arrange the tomatoes and plums on a serving platter, alternating the tomatoes and plums. Tear the buratta over the top. Sprinkle the basil and mint over the salad and then drizzle with the vinaigrette. Finish with a pinch of sea salt and some pepper; serve.