You need grill pans without holes or, alternatively, skewers.
Put the squeezed garlic, oil, lime juice, sugar, and spices in a large bowl. Cut the vegetables into bite-sized pieces that can also be skewered. Add everything to the sauce and mix well. You can vary the vegetables, of course, and you can also add what has to go.
I leave it in the refrigerator for about 4 to 5 hours so that the vegetables can cook through completely.
On our charcoal grill, the vegetables in the grill pans take about 15-20 minutes to cook. We add some of the sauce so that the vegetables can simmer in the sauce.