Preheat a grill to medium high and prepare for indirect cooking: On a gas grill, turn off half the burners; on a charcoal grill, bank the coals to one side.
When the grill registers 375˚ F to 400˚ F, brush the zucchini, bell peppers, cabbage and eggplant all over with olive oil and season generously with kosher salt and pepper. Place the vegetables on the cooler side of the grill (indirect heat) with the larger end of the eggplant closest to the direct heat. Cover the grill and cook for 40 minutes. Flip the vegetables, then continue to cook, covered, until you can insert a skewer into the center of each vegetable with little to no resistance (start checking for doneness after 30 more minutes — it may take longer, depending on your grill). Remove the vegetables to a board or platter as they are ready and let rest 15 to 20 minutes.
Slice the vegetables, drizzle with olive oil and vinegar and top with herbs, chiles and flaky sea salt.
When you’re grilling whole vegetables that are uneven in size, place the thicker part closer to the heat source.