Thinly slice the yellow onion into uniform half-moons.
Heat 0.5 tsp of olive oil in a skillet over medium-low heat, add the onions and a pinch of salt, and cook for 15 minutes until deeply caramelized.
Stir the balsamic vinegar into the onions to deglaze the pan, cook for 1 more minute, then set the onions aside.
Season the flank steak on both sides with sea salt and black pepper.
Wipe the skillet clean, add the remaining 0.5 tsp of olive oil, and increase heat to medium-high.
Sear the steak for 3-4 minutes per side for medium-rare, then transfer to a cutting board to rest for 5 minutes.
Toast the sourdough slice until golden and spread the Dijon mustard evenly across the surface.
Thinly slice the steak against the grain to ensure maximum tenderness.
Assemble the sandwich by layering the arugula, sliced steak, and caramelized onions onto the toasted sourdough.