Preheat the broiler and position a rack 8 inches from the heat. In a large skillet, heat the olive oil. Add the broccoli and garlic and cook over moderate heat, stirring occasionally, until the broccoli is browned in spots and crisp-tender, about 5 minutes. Stir in the spices and oregano. Season with salt and cook for 1 minute. Add 1/2 cup of water and cook until the broccoli is tender and the liquid has evaporated, about 3 minutes.
Arrange half of the cheese in 6 individual gratin dishes. Top with the broccoli and the remaining cheese. Broil for 5 to 6 minutes, or until the cheese is melted and browned. Serve right away with warm tortillas.