For the horseradish sauce:

1. Make the horseradish sauce by combining all sauce ingredients and stirring well to combine. Cover and let sit in refrigerator until ready to use.

For the steak sandwiches:

1. Preheat grill over medium-high heat.
2. Season steak with steak seasoning.
3. Lightly brush with 1 tablespoon of olive oil. Let sit at room temperature for 20 minutes.
4. Meanwhile, toss onions with additional 2 tablespoons olive oil and season them with salt and pepper.
5. Place onions in a grilling pan or wrap in foil.
6. Place on grill and cook until onions are softened and beginning to caramelize, about 25 minutes.
7. Once steak has sat at room temperature for 20 minutes, place on grill.
8. Cook for 4-5 minutes, until steak is golden and has grill marks and then flip. For medium-rare, cook until 140 degrees F or another 3-4 minutes, for medium cook until 150-155 degrees F or another 5-6 minutes, and for medium-well cook until 160-165 degrees F or another 6-7 minutes. This always depends on the thickness of your steak. To be sure, use a meat thermometer.
9. Let your steak rest for 3 minutes before slicing.
10. While steak is resting, butter the buns.
11. Place bun halves on grill, butter side down, and lightly grill for 1-2 minutes. Keep a close eye on them as they will burn easily.
12. Once steak has rested, cut it as thinly as possible.
13. Place approximately 2 tablespoons of spread on the bottom half of each bun.
14. Top with steak and onions.
15. Top with arugula and finally the top half of the bun.
16. Serve and enjoy!