1: Trim off any blemished leaves from the heads of cabbage and core. Slice each cabbage into wedges, using bamboo skewers to hold them together. Place on a rimmed baking sheet. Brush each wedge (cut sides) with olive oil and season with salt and pepper. Repeat on the other side.

2: Set up your grill for direct grilling and heat to medium-high. Brush or scrape the grill grate clean and oil it well. Arrange the cabbage wedges, cut sides down, on the grate. Grill for 3 to 4 minutes per side, or until the outside shows some char but the inside is still raw and crisp. Let cool, then thinly slice the cabbage.

3: In the meantime, make the dressing: In a large bowl, combine the salt, pepper, celery seed, brown sugar, and red wine vinegar. Whisk to dissolve the salt, then slowly whisk in the olive oil. Taste for seasoning, adding more salt, pepper, sugar, or vinegar to taste. Stir in the sliced cabbage, coating with the dressing. Can be chilled or served at room temperature. Cover and refrigerate any leftovers for up to 1 day.