Prep the steak (5 minutes): Pat the steak dry with paper towels. Season with kosher salt, pepper, and steak seasoning. Let it sit at room temperature for 15–20 minutes.
Caramelize the onions (15 minutes): In a cast iron skillet over medium heat, melt butter with olive oil. Add sliced red onions and a pinch of salt. Cook, stirring occasionally, until softened and golden brown. Remove from skillet and set aside.
Cook the steak (8–10 minutes): Heat the skillet over medium-high heat. Add olive oil. Sear steak for 3–4 minutes per side, depending on thickness, until medium-rare or your desired doneness. Use a meat thermometer if needed (130°F for medium-rare).
Rest and slice (5 minutes): Transfer steak to a cutting board. Rest for 5 minutes, then slice the steak against the grain into thin slices.
Make horseradish sauce (2 minutes): In a small bowl, mix sour cream, horseradish, lemon juice, salt, and pepper. Stir until smooth.
Toast the bread (2–3 minutes): While the steak rests, toast sandwich rolls in the skillet until golden brown.
Assemble the sandwiches (3 minutes): Spread horseradish sauce on bread, layer with sliced steak, caramelized onions, cheese, and greens. Close sandwich and serve warm.