Place the ground beef in a bowl. Add 1 tsp salt, 1/2 tsp black pepper, 1 tbsp Worcestershire sauce, and 1/2 tsp onion powder. Mix gently with your hands until just combined — do not overwork. Divide into 4 equal portions and form into thin, slightly larger-than-bread-diameter patties (each about 3/8–1/2 inch thick). Make a shallow dimple in the center of each patty with your thumb to reduce doming while cooking.

Cook patties

Heat a heavy skillet or cast-iron pan over medium-high heat and add 1 tbsp vegetable oil or butter. When shimmering, add patties (work in a single layer; cook in two batches if needed). Cook for 3 minutes on the first side without moving, flip, and cook 2–3 minutes more for medium (adjust time for preferred doneness). If you want the cheese melted on the patty, place a slice of Swiss on each cooked patty in the pan and cover for 30–45 seconds to melt. Transfer cooked patties to a plate and tent with foil to rest briefly.

Caramelized Onions

Slice onions

While patties rest or before cooking patties, peel and halve the onion. Slice into 1/8–1/4-inch thin half-moons.

Caramelize

In a separate skillet, heat 1 tbsp butter and 1 tsp vegetable oil over medium-low heat. Add sliced onions, 1/4 tsp salt, and 1/2 tsp brown sugar (optional). Stir to coat. Cook slowly, stirring every 2–3 minutes, for 20–25 minutes until onions are deep golden brown and sweet. If they start to stick, add 1–2 tbsp water to deglaze. Remove from heat and keep warm.

Russian-style Sauce (for spread)

In a small bowl, whisk together 1/4 cup mayonnaise, 2 tsp ketchup, 1 tsp prepared horseradish or Dijon mustard, 1 tbsp pickle relish, 1/4 tsp paprika, 1/2 tsp lemon juice and 1/8 tsp black pepper. Taste and adjust — add more relish for tang, more horseradish for heat, or a pinch of sugar if you prefer sweeter. Refrigerate until ready to assemble.

Assembly

Butter bread and preheat pan

Heat a clean skillet or griddle over medium heat. Spread softened butter evenly on one side of each slice of bread (8 slices). The buttered sides will be the exterior for grilling.

Assemble sandwiches

On the unbuttered side of 4 bread slices, spread a generous tablespoon of the prepared sauce. Place a cheese-topped patty on each, then divide the caramelized onions evenly over the patties. Add a second slice of Swiss on top of the onions if you like extra cheese. Top each with the remaining bread slice, buttered side out.

Grill sandwiches

Place sandwiches in the preheated skillet. Cook 3–4 minutes per side over medium heat, pressing gently with a spatula or a sandwich press until the bread is deep golden brown and the cheese is melted. If the bread browns too quickly before the cheese melts, lower the heat and cover the pan for 1–2 minutes.

Serve

Remove sandwiches from the pan, let rest 1 minute, then slice in half diagonally. Serve hot with extra sauce or pickles on the side.