Pat the beef knuckle roast (sirloin tip roast) dry. In a small bowl, mix together the kosher salt (for roast), black pepper (for roast), garlic, Dijon mustard, olive oil (for roast), rosemary, and thyme leaves to form a paste. Rub all over the roast and let stand at room temperature for 30 minutes while you heat the oven to 450Β°F.
Start the onions: Warm the unsalted butter and olive oil (for onions) in a large skillet over medium-low heat. Add the yellow onions and the kosher salt (for onions). Cook, stirring occasionally, until deeply golden and soft, 25β35 minutes; if the pan looks dry, add a splash of the water. Deglaze with the remaining water and the apple cider vinegar, scraping up browned bits, then cook until jammy, 2β3 minutes more. Keep warm over low heat.
Roast the meat: Set the roast on a rack over a rimmed baking sheet. Roast at 450Β°F for 15 minutes, then reduce the oven to 275Β°F and continue roasting until the center reaches 125Β°F for medium-rare, about 45β75 minutes more depending on thickness. Transfer to a cutting board and rest for 20 minutes.
Make the horseradish sauce: In a small bowl, stir together the mayonnaise, prepared horseradish, lemon juice, black pepper (for sauce), and kosher salt (for sauce). Refrigerate until ready to use.
Slice the meat: Using a sharp knife, thinly slice the roast across the grain into very thin slices, catching any juices on the board.
Toast the bread: Arrange the sandwich rolls, cut sides up, on a baking sheet. Brush the cut sides with the olive oil (for toasting rolls) and toast in the 350β400Β°F oven until the edges are lightly crisp, 3β5 minutes.
Assemble: Spread the cut sides of the rolls with horseradish sauce. Layer arugula on the bottoms, pile on warm sliced beef, and top with a generous spoonful of caramelized onions. Cap with the top rolls, press gently, slice if desired, and serve immediately.