Thinly slice the yellow onion into half-moons.
Heat half of the olive oil in a skillet over medium heat and sauté the onions for 10-12 minutes until soft and golden brown, stirring in the balsamic vinegar during the last minute.
Pat the steak dry with a paper towel and season both sides evenly with sea salt and black pepper.
Remove onions from the skillet, increase heat to medium-high, and add the remaining olive oil.
Sear the steak for 3 to 4 minutes per side for medium-rare, then transfer to a cutting board to rest for at least 5 minutes.
While the steak rests, toast the sourdough slices in the same skillet or a toaster until they reach a golden brown color.
Thinly slice the rested steak against the grain into bite-sized strips.
Spread the Dijon mustard onto one slice of toasted bread, then layer the sliced steak, caramelized onions, and baby arugula before topping with the second slice of bread.