For burger sauce, mix together mustards and mayonnaise; set aside.
Divide meat into quarters (about 4 ounces each) and roll into balls. Transfer to a plate or small baking sheet.
Heat a large (12-inch) cast-iron, stainless steel, or carbon steel skillet over medium-high heat until ripping hot and smoking, about 5 minutes.
Toast half of the buns, cut side down, in skillet until lightly golden, about 1 minute. Repeat with remaining buns.
Increase heat to high.
Add two beef balls to skillet; season generously with kosher salt. Smash beef balls down with a heavy duty spatula, using a potato masher to press down on top of the spatula for extra leverage, until very thin, about ½-inch thick. Cook, without moving, until bottom sides are crisp and browned, about 1 ½ minutes.
Press a few onion slices into burger patties with spatula. Scrape up and flip patty.
Place a slice of cheese over burger and continue to cook until cheese is melted and onions on bottom are griddled and golden, 30–60 seconds. Remove from griddle.
To assemble, spread 1 tablespoon burger sauce on cuts sides of buns (tops and bottoms). Cover bottom buns with pickle slices then top with burger patty. Add a few slices of raw onion, a couple of folded sheets of iceberg lettuce followed by the top bun.
Wipe out skillet with paper towels before repeating smashing and cooking process with remaining beef balls, onions and cheese.
Serve burgers with pickle spears.