Preheat your oven to 425°F (218°C). While the oven heats, cut the cabbage into 8 equal wedges, making sure each wedge has a piece of the core to hold it together.
Arrange the cabbage wedges in a single layer on a large, rimmed baking sheet. Drizzle the 1/3 cup of olive oil evenly over the wedges, making sure to coat the sides and tops.
Season the cabbage evenly with the 1 teaspoon of kosher salt and 1/2 teaspoon of black pepper. Turn the wedges over to ensure both sides are well seasoned.
Roast on the middle oven rack for 20 minutes. The edges should begin to turn golden brown and become slightly crispy.
Carefully remove the pan from the oven and flip each wedge over with a spatula. Evenly sprinkle the minced anchovies, chopped walnuts, and grated Parmesan cheese over the wedges.
Return the pan to the oven and roast for another 10-15 minutes, or until the cabbage is tender when pierced with a fork, the walnuts are toasted, and the cheese is melted and golden.