Chili Burgers with Southern-Style Slaw, Mustard and Onions

Ingredients

• 2 tablespoons fine sugar
• 3 tablespoons cider vinegar
• 3 tablespoons vegetable oil, divided
• 1 teaspoon celery salt
• 1 small carrot, grated
• 2 cups grated or shredded cabbage
• 1 pound ground beef or turkey
• Salt
• pepper
• 1/4 cup grated onion
• 2 cloves garlic, grated or pasted
• 1/2 tablespoon ground cumin
• 1/2 tablespoon green or red chili powder, such as Gebhart's
• 2 4-ounce cans green chilies, drained
• 1/2 cup loosely packed cilantro, chopped
• 4 slices Monterey Jack or white American cheese
• 4 slices Pepper Jack cheese
• 4 brioche rolls, split and toasted
• Yellow mustard, for serving
• Chopped raw onion, for serving