Start with a firm head of green or red cabbage (~2 lbs). Remove any wilted outer leaves. Stand upright, halve through the stem, then cut each half into 2-inch wedges. Keep the core and stem intact — this holds the wedge together on the grates. Trim the stem base flat if needed, but don't remove it. Brush all sides generously with olive oil, then season with salt and pepper at minimum. For more flavor, use a simple marinade of olive oil, minced garlic, salt, pepper, and chili flakes. Apply any Parmesan-based coating just before grilling.

Preheat a gas grill to 400°F or set up a two-zone charcoal fire. Clean the grates before starting. Gas grill (single-zone): Place wedges cut side down over direct heat. Cook first cut side 5–6 min undisturbed, flip to second cut side for another 5–6 min. Total: 10–12 min. Charcoal (two-zone): Cook each of the three flat surfaces 2 min over direct heat, lid closed. Once all sides are charred (~6 min), move to the cooler side and cook 4 more min indirect. Total: ~10 min. Overall range is 10–16 min depending on wedge thickness and how tender you want the center. Keep the lid closed throughout.

Done when cut surfaces are deeply charred and caramelized, outer leaves soft and smoky, center still slightly crunchy — that contrast is the goal. For fully tender throughout, add a few more minutes on the indirect side. Serve immediately off the grill. Finish with balsamic glaze, Parmesan, fresh parsley, or a warm vinaigrette with vinegar, olive oil, and crisped pancetta poured over the hot wedges. Avoid: removing the core before grilling (wedge falls apart), moving wedges too soon (kills the sear), too much oil (flare-ups, greasy flavor), cooking entirely over high direct heat (burns outside, raw center).