Slice the beef as thinly as possible, about 1/8-inch thick; freezing the beef for 30 minutes before slicing makes this much easier. Slice the onions into 1/4-inch pieces and mince the garlic and ginger.

In a small bowl, whisk together soy sauce, mirin, sugar, and sake until the sugar dissolves completely.

Heat a large skillet over medium-high heat for 2 minutes, then add 1 tablespoon of oil and swirl to coat evenly.

Add the sliced beef in a single layer and let it sear without moving for 45 seconds until lightly browned on one side. Stir and cook for another 30 seconds until the beef is just cooked through, then transfer to a clean plate.

Add the remaining 1 tablespoon of oil to the same skillet and add the onions, stirring occasionally for 5 to 7 minutes until they become golden and slightly translucent.

Push the onions to the side and add the minced garlic and ginger to the cleared space, stirring for about 30 seconds until fragrant.

Pour the sauce mixture into the skillet and bring it to a gentle simmer, stirring to combine with the onions and aromatics. Return the beef to the pan along with any juices that accumulated on the plate, and toss gently for another minute until everything is coated and heated through.

Divide the warm cooked rice among serving bowls and top each portion with the beef and onion mixture, spooning extra sauce over everything. Garnish with green onions and sesame seeds if desired.