In a mixing bowl, whisk together sugar, vinegar, 2 tablespoons oil and celery salt. Add carrot and cabbage; toss to combine.
Mix meat with salt, pepper, onion, garlic, cumin, chili powder, green chilies and cilantro. Form into 4 patties that are thinner at center and thicker at edges for even cooking.
Heat a skillet over medium-high heat with remaining tablespoon of vegetable oil. Cook patties 8 minutes, turning occasionally. Melt a slice of each of the 2 cheeses over each patty in last 2 minutes of cooking time.
Serve patties on toasted rolls topped with slaw, some yellow mustard and raw onions.
Serve with tater tots or oven fries alongside with barbecue sauce or ketchup for dipping taters.