In a skillet, melt the butter and add the sliced onions. Toss the onions well in the butter and season with salt and pepper. Cook, stirring occasionally, until the onions are deeply golden brown and then set aside.
Whisk all the horseradish sauce ingredients together until smooth and refrigerate until ready to use.
About 30 minutes before you plan to cook, season the steaks with salt and pepper and let them sit at room temperature.
Preheat a grill or grill pan over medium-high heat. For medium temperature, grill the steak for 4-5 minutes per side for thicker steaks, 3-4 minutes for thinner steaks. Cook longer for medium-well or well-done steaks. Transfer to a plate and tent with foil.
After the steak has rested, thinly slice it and lightly season with flaky sea salt if desired.
Grill the bread, cut side down, for 1-2 minutes. Assemble the sandwiches by spreading the horseradish sauce on both sides. Add the caramelized onions, sliced steak, brie slices, and top with arugula and radishes. Top with the other slice of bread and serve immediately.