01 -
Stir together all burger sauce ingredients in a small bowl. Cover, and chill until ready to use.
02 -
Divide beef into 8 (3-ounce) portions, and shape each portion into a loose ball; place on a plate. Cover, and chill while preparing grill.
03 -
Cut a 3-inch square of parchment paper; set aside. Preheat grill to high (450°F to 500°F); place a large cast-iron skillet or griddle on the grill to preheat. (Alternatively, heat a large cast-iron skillet or griddle on the stove over high.).
04 -
Drizzle skillet evenly with oil. Working in batches if needed, arrange onion slices in 8 small mounds (about 1/4 cup each) on the skillet, spacing at least 2 inches apart. Top onion mounds with jalapeño slices (about 1 tablespoon each), and sprinkle evenly with 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook, undisturbed, until onions are beginning to brown, 30 seconds to 1 minute.
05 -
Place 1 meatball on each onion mound. Top with parchment paper square, and press firmly to flatten, using a sturdy spatula or burger press, to form a 4-inch-wide patty; remove parchment paper. Repeat process with remaining meatballs and onion mounds. Sprinkle smashed patties evenly with remaining 3/4 teaspoon salt and remaining 1/2 teaspoon pepper. Cook, undisturbed, until patties begin to crisp around the edges, 2 to 3 minutes.
06 -
Flip patties so that the onion-jalapeño mixture is on top. Place 1 cheese slice on each of 4 patties. Continue to cook until patties are well browned and cheese is melted, 1 minute and 30 seconds to 2 minutes. Top each cheese-covered patty with a plain patty to create 4 double stacks. Transfer each stack to a bottom bun. Spread about 1 tablespoon of burger sauce on each top bun; place on top of patties. Serve immediately.