2 1/2 tablespoons mayonnaise
2 tablespoons sour cream
1 1/2 tablespoons ketchup
1 tablespoon dill pickle relish
2 teaspoons fresh juice from 1 lemon
1 teaspoon grated horseradish from a jar
Kosher salt and freshly ground black pepper
8 small thin slices Jewish rye bread, or 4 large thin slices Jewish rye bread cut in half
3 tablespoons unsalted butter, softened
3 tablespoons vegetable oil
1 pound freshly ground beef chuck, preferably about 80 percent lean, formed into 4 (4-ounce) balls
Ground coriander seed, for sprinkling
1/2 cup drained sauerkraut
8 thin slices Swiss cheese, divided
Preheat oven to 350°F.
In a medium bowl, stir together mayonnaise, sour cream, ketchup, relish, lemon juice, and horseradish. Season Russian dressing with salt and pepper and set aside.
Brush rye bread with softened butter and set on a rimmed baking sheet in 1 layer. Bake in oven until toasted, turning once, about 5 minutes.
Heat oil in 2 large skillets or 1 large cast iron griddle over high heat until smoking.
Season beef balls all over with salt and pepper and add to skillets or griddle, spacing them apart. Using a sturdy metal spatula, smash each ball to a thin round patty.
Sprinkle with coriander seed and cook until well browned and crusty on the bottom, 2-4 minutes.
Top each patty with sauerkraut, then scrape patties from skillet using a sturdy thin metal spatula or metal bench scraper, and flip so that sauerkraut is on bottom side.
Top each patty with 1 slice of Swiss cheese and cook until kraut is softened and browned slightly and cheese has melted.
Meanwhile, set remaining 4 slices Swiss cheese on half of bread slices and return to oven to warm bread and melt cheese, about 1 minute. Set cheese-topped bread slices on patties, cheese side down.
Spread Russian dressing on the 4 remaining bread slices, reserving any remaining dressing for another use. Lift each burger stack and set on top of bottom bread with Russian dressing.