Thinly slice the yellow onion into half-moons.
Heat 0.5 tsp of olive oil in a non-stick skillet over medium-low heat.
Add the onions and cook, stirring occasionally, for 15 minutes until golden brown and sweet.
Stir in the balsamic vinegar during the last minute of cooking the onions, then remove from the pan and set aside.
Season the flank steak on both sides with sea salt and black pepper.
Wipe the skillet and heat the remaining 0.5 tsp of olive oil over medium-high heat.
Sear the steak for 3 to 4 minutes per side for medium-rare, then transfer to a cutting board to rest for 5 minutes.
While the steak rests, toast the sourdough slices until they are crisp and golden.
Slice the steak thinly against the grain to ensure maximum tenderness.
Spread the Dijon mustard on one slice of toast, then layer with the sliced steak, caramelized onions, and fresh arugula before topping with the second slice.