Cut the cabbage in half lengthwise, then cook in a pot of boiling salted water until tender, 15 to 20 minutes. Remove the cabbage and let cool to warm.
While the cabbage is cooking, mash the garlic to a paste with a large pinch of salt, then add the anchovy to the garlic and continue to mash and mince to incorporate the anchovy. Transfer the garlic-anchovy paste to a bowl. Whisk the egg yolk and lemon juice into the garlic-anchovy paste, then slowly whisk the oil into the dressing until it is emulsified. Season the dressing with salt and pepper to taste.
Preheat the grill.
Cut the cabbage into wedges, then brush with some of the dressing. Grill the cabbage until it has grill marks, then transfer to a serving plate and drizzle with additional dressing. Serve.
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