Heat the oven to 200˚C / 400˚F.
Place the nectarines and/or peaches and tomatoes onto a baking sheet and drizzle with 2 tablespoons of olive oil and add the vinegar, 1/2 teaspoon of salt and season with black pepper. Toss to coat and roast until the fruit is very soft, 25 to 30 minutes.
Meanwhile, heat a large skillet on medium high until hot. Add 1 to 2 tablespoons of olive oil and add the gnocchi. Season with salt and pepper and cook undisturbed for 2 to 3 minutes to allow them to get golden and crispy. Toss, and leave to cook undisturbed again, until the gnocchi are golden in many parts, another 2 to 3 minutes.
To serve, place the gnocchi onto a deep plate or shallow bowl, top with the roasted stonefruit and tomatoes. Tear the burrata and drape it over the fruit and gnocchi. If using, scatter over the umeboshi. Drizzle with more olive oil and top with basil. Finish with a gentle scatter of salt and black pepper. Serve immediately.