Line a baking sheet with foil, and grease with a few teaspoons of vegetable oil. Arrange cabbage slices, cut side up if possible, on the sheet, and drizzle remaining vegetable oil evenly over cabbage.

Set an oven rack about 7 inches from the heat source and preheat the oven's broiler.

Broil until the surface of cabbage is lightly charred, 4 to 6 minutes. Times will vary depending on your oven, so watch closely during each charring step.

Use a spatula and tongs to turn cabbage over; return to the broiler to char the other side of cabbage, 3 to 6 minutes.

Once both sides of cabbage are lightly charred, scatter over sliced onions and use a vegetable peeler to make long, thick strips of carrot over the top. Arrange carrot strips evenly on top, and return pan to the broiler.

Broil until carrots and onions begin to soften, about 3 minutes.

Sprinkle salt, garam masala (or curry powder), and cayenne. Use tongs to mix evenly. Use a spatula to move vegetables in from the edges of the pan to remove empty space and form an even rectangle.

Return pan to the broiler; broil until cabbage is tender, and is charred to your liking, a few minutes more.