This burger is the epitome of Texas. The flavorful pork patties are studded with chopped green chilies, adding moisture and just the right amount of heat. For the best sear, we use a cast-iron skillet. The flat, even heat gives your burgers a uniformly browned crust and allows the meat to cook in its own fat, enhancing the flavor. You can make this recipe inside on your stove-top, or put the skillet right on the grate of a hot grill. We promise: once you try this method, there’s no going back.
Make the slaw In a large bowl, whisk the mayonnaise with the lime juice and garlic. Season with salt and pepper. Add the cabbage and carrot and toss to coat. Cover and refrigerate while you prepare the burgers.
Make the burgers In a large bowl, gently combine the pork with the green chilies, cilantro, cumin and 1 teaspoon of salt. Form the pork into four 4-inch wide and ¾-inch- thick patties; season lightly with salt. Transfer to a plate.
On a grill or stovetop, heat a 12-inch cast-iron skillet over moderately-high heat. Add the oil. When the oil is shimmering, add the pork patties, being sure not to crowd them. If they are touching, then they won’t sear well. If necessary, cook in batches. Cook the burgers over moderately-high heat until a deep brown crust has formed, 4 to 6 minutes. Flip the burgers, top each patty with a slice of cheese and cook until browned and just cooked through, about 4 minutes more. Transfer the pork burgers to the bottom halves of the toasted buns and let rest for 5 minutes.
Meanwhile, add the cilantro and scallions to the slaw and give it one more toss. Season with salt and pepper.
Top each burger with a few slices of avocado and a generous pile of red cabbage slaw. Close the burgers and serve, passing hot sauce at the table.