In a food processor or blender, puree together the mayonnaise, vinegar, garlic, and basil leaves until smooth. Season, to taste, with salt and freshly ground pepper.
Place a tortilla on a flat surface and spread with basil mayonnaise. Arrange 1 or 2 layers of the grilled vegetables over the tortilla. Sprinkle with a 1/4 cup of the cheese. Tightly roll up the tortilla and secure with a toothpick. Cut into 4 pieces. Repeat process for remaining tortilla and vegetables.