1. Place the grapes, preferably red, in a medium bowl with the vinegar, olive oil, garlic, sugar, about 2 g of fennel seeds, about 1 g of flaky salt, and plenty of black pepper. Mix well and set aside to marinate.
2. Thread the washed grapes onto skewers; you should place about five or six grapes on each skewer. Do not discard the marinade, as you will use it when serving.
3. Heat a grill or barbecue over high heat. Once the grill is very hot, add the grape skewers a couple at a time and grill them for about 2–3 minutes, turning them halfway through cooking. Remove them from the heat once they are lightly charred.
4. When ready to serve, cut the burrata in half and place one half on each plate. Arrange the grape skewers leaning against the burrata—two skewers per serving—and spoon about 7–8 g of the marinade over the burrata. Alternatively, arrange everything on a serving platter to share.
5. Finally, sprinkle over the remaining fennel seeds, garnish with a sprig of basil, and serve.