Preheat a grill for medium-high heat.
Combine the garlic, Parmesan, 1/4 cup of the olive oil, lemon juice, mayonnaise, Dijon, anchovy paste if using, white wine vinegar, Worcestershire, 1/4 teaspoon salt and several grinds of pepper in a blender.
Blend on high speed until smooth and creamy, scraping down the sides of the blender carafe with a rubber spatula as necessary. Taste and adjust the seasoning with more salt and pepper. Transfer the Caesar dressing to a small bowl, cover with plastic wrap and refrigerate until ready to serve, up to 1 day.
Cut the cabbage through the core into 8 long wedges (each wedge should be 1 1/2 to 2 inches thick).
Make sure to keep the core intact, as this will hold the wedges together as they cook. Brush the cabbage wedges and sliced bread with the remaining 3 tablespoons of olive oil and season with a pinch each of salt and pepper.
Lightly oil the hot grill grates. Place the cabbage on the grill and cook, covered, until the first side is nicely charred, about 5 minutes. Flip the cabbage, then continue to cook, covered, until crisp-tender and nicely charred all over, about 5 minutes more. Transfer to a serving platter. Place the bread on the grill and cook uncovered until toasted and golden brown, 1 to 2 minutes per side.
Tear or cut the bread into 1-inch cubes, then sprinkle over the grilled cabbage. Drizzle with most of the Caesar dressing, then top with some shaved Parmesan and more pepper. Serve the remaining dressing on the side. |