Pit the stone fruit and cut into irregular pieces. Transfer to a serving platter, then sprinkle with the lemon juice, sugar and ½ teaspoon flaky sea salt. Toss with your hands, then let sit until juices pool on the platter, 5 to 10 minutes. Taste and adjust sugar, salt and lemon juice until the fruit tastes perky and bright — like the greatest stone fruit you’ve eaten.
Tear the mozzarella into bite-size pieces and nestle it among the fruit. Tuck in the herb leaves. Drizzle the platter with olive oil. If the cheese looks dry, add a little more oil. Sprinkle with a few grinds of black pepper and a pinch of flaky salt, and serve.
