Brush both sides of each cabbage wedge with olive oil. Sprinkle garlic powder, red pepper flakes, savory, salt, and pepper over each wedge. Arrange on a baking sheet.
Roast in the preheated oven for 15 minutes covered with foil; flip cabbage (add grated cheese if desired) and continue to roast uncovered until browned and charred in some areas, about 15 more minutes.