Prepare the grill for direct cooking over medium heat (350° to 450°F).
In a small bowl combine the cumin, 1 teaspoon salt, and 1 teaspoon pepper. Lightly brush the steaks on both sides with oil and season evenly with the spices. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
Grill the steaks over direct medium heat, with the lid closed, until cooked to medium-rare doneness, 4 to 6 minutes, turning once. Remove from the grill and let rest for 3 to 5 minutes. Cut the steaks into ½-inch pieces.
In a large saucepan over medium heat, warm 1 tablespoon oil. Add the onion and garlic and cook until the onion is tender, about 5 minutes, stirring occasionally. Stir in the chili powder and oregano and cook until fragrant, 1 to 2 minutes. Add the remaining chili ingredients and increase the heat to bring the chili to a boil. Reduce the heat to low, add the steak, cover, and simmer for 20 minutes. Uncover the pan and continue to simmer until the chili thickens to the consistency you like, 40 to 50 minutes, stirring to the bottom of the pan occasionally. Season with salt and pepper. Serve warm topped with grated cheese.