Thinly slice the yellow onion into half-moons.
Heat 0.5 tsp of olive oil in a skillet over medium-low heat and add the onions, cooking slowly until they become soft and golden brown, approximately 15 minutes.
Stir the balsamic vinegar into the onions to deglaze the pan, then remove the onions and set them aside.
Season the flank steak evenly on both sides with sea salt and black pepper.
Wipe out the skillet, increase the heat to medium-high, and add the remaining 0.5 tsp of olive oil.
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 sprouted grain bread slices until they are golden and crisp.
Slice the rested steak thinly against the grain to ensure maximum tenderness.
Spread Dijon mustard onto one slice of toast, then layer with arugula, the sliced steak, and the caramelized onions before topping with the second slice of bread.