Pour mustard vinaigrette into a mixing bowl. Add cucumbers and arugula on top. Set aside until ready to serve.
Heat a large skillet or grill pan with cooking oil over medium heat. Add burger patties and sear on both sides until they reach an internal temperature of 165F / 74C degrees, ~5 minutes on each side.
Remove burger patties from heat and allow to rest for 1 to 2 minutes.
Toss salad and divide between serving bowls. Add burger patties and sauerkraut. Enjoy!