GET THE GRILL READY: Set grill for direct medium heat (350 degrees). Brush grates clean or use a grill pan or basket.
PREP THE ZUCCHINI: Meanwhile, in a medium bowl, toss together the zucchini, salt, pepper, garlic, and oil.
GRILL THE ZUCCHINI on one side (lid closed) until grill marks appear—about 3 minutes. Turn the zucchini coins over.
ADD CHEESE/GRILL/TURN/REPEAT: Add a small pinch grated Parmigiano-Reggiano to the grilled side of each zucchini coin. When melted, and the second side is then browned, turn the zucchini over again. To the second side, add the same small pinch of grated Parmigiano-Reggiano to each coin and let the cheese melt. Turn zucchini again and you’ll see the crispy cheese on top now. Grill for a minute or so, then turn the zucchini one last time and the second side comes up cheesy-crispy, too.
SERVE HOT, WARM, AT ROOM TEMP, OR COLD as an appetizer or as a side. If an appetizer, you might consider a dip such as a small cup of marinara sauce, pesto, or aioli.