Steam the potatoes until soft, but do not overcook.
In a large zippered plastic bag, combine apple juice, vinegar, basil, mustard, honey, soy sauce, oil, garlic and black pepper. Put mushrooms, red pepper, zucchini and boiled potatoes in a bag with dressing. Fasten the bag and shake well, put in the refrigerator for 2 hours.
Grease the grill grate with vegetable oil and turn on the grill to preheat to medium temperature. Remove the vegetables from the marinade and string them in turn on 4 metal or wooden sticks. Place the kebabs on the oiled wire rack.
Close the grill and cook the kebabs for 10-15 minutes, periodically turning the kebabs and brushing with marinade.