Preheat your oven to 325°, line a baking sheet with foil, and top with a wire rack.

Rub the beef sirloin roast with olive oil, then season with salt, black pepper, granulated onion, and garlic.

Place the beef onto the wire rack and insert a digital thermometer into the thickest part of the roast. Roast for about 1 hour and 15 minutes, until the thermometer registers 125° to 135° for medium-rare to medium doneness.

Allow the beef to rest for about 15 minutes before slicing very thinly.

(Optional) In a skillet over medium-high heat, drizzled with oil, add sliced onions with a pinch of salt and pepper. Sauté for 15 to 20 minutes until deeply brown and caramelized. Set aside.

In a small pot over medium-low heat, melt the butter. Stir in the flour to create a roux and cook for about 1 minute.

Whisk in the milk until smooth, and cook for 5 to 10 minutes, stirring frequently, until it begins to thicken.

Remove from heat and slowly whisk in the grated cheddar cheese until smooth. Add granulated onion, ground mustard, paprika, and salt, and adjust seasoning as needed.

If using, spread horseradish sauce on toasted onion buns. Assemble sandwiches by layering sliced roast beef, cheddar sauce, and caramelized onions between the buns. Cover with the top bun and serve.