Thinly slice the yellow onion into half-moons.
Heat 0.5 tsp of ghee in a non-stick skillet over medium-low heat; add the onions and cook, stirring occasionally, until they are soft and golden brown, about 12-15 minutes.
Stir in the balsamic vinegar to deglaze the pan, cooking for 1 more minute until the liquid is absorbed, then remove onions from the skillet.
Pat the steak dry with a paper towel and season both sides with sea salt and black pepper.
Increase the skillet heat to medium-high and add the remaining 0.5 tsp of ghee.
Sear the steak for 3-4 minutes per side for a medium-rare finish, then transfer to a cutting board to rest for at least 5 minutes.
While the steak rests, toast the sourdough bread until the edges are golden and crisp.
Slice the rested steak thinly against the grain.
Spread the Dijon mustard onto the toasted sourdough, then layer with baby arugula, the sliced steak, and the caramelized onions.