Trim the steak of any excess fat. Slice steak into 1/4-inch strips and pat dry with a paper towel.
In a medium bowl, combine sugar, sesame oil, 1 tsp. soy sauce, and 1 tsp. salt. Add sliced steak strips, stir to coat, and let it sit for 20 minutes.
Slice onions into rounds with a sharp knife, and peel and thinly slice ginger using a manxdolin or sharp knife.
Place a large skillet over high heat. Pour in vegetable oil and swirl to coat bottom of pan. The oil should be shimmering and you should see some wisps of smoke. If the pan is not hot enough, the meat will steam instead of getting deeply browned.
Add the steak to the skillet in an even layer. It’s okay to crowd it a bit. Cook, undisturbed, until brown around the edges, about 2 minutes. Turn steak over and add onion, ginger, lots of pepper, and 1/3 cup water. Cook, tossing often, until onion is just tender and ginger is softened, about 2 minutes.
Remove skillet from heat and add butter, lemon juice, and remaining 1 tablespoon of soy sauce. Toss until butter is melted and coats steak. Taste and season with more salt if needed.
Serve over cooked rice.