Mix the vinaigrette in a bowl and add the grapes. Let them sit 30 minutes or as long as you like.
Thread each wooden skewer with 6 grapes each, saving the vinaigrette for the cheese.
Use a grill pan on the stove. Grill about 1-2 minutes per side in a hot grill pan.
Lay the balls of mozzarella or burrata on a platter and decorate with the grilled grape skewers.
Drizzle the remaining vinaigrette over the cheese and grapes. Scatter with basil leaves.
