Place the sesame seeds into a large skillet over medium heat, and cook and stir constantly until the seeds are toasted a golden brown and make a continuous crackling noise, 1 to 2 minutes. Transfer the seeds immediately to a bowl to stop the cooking process. Set seeds aside.
Place sesame oil in the hot skillet, and heat until it just begins to smoke (this should happen very fast). Place mustard greens into the hot oil, and pour in water. With a spatula, gently toss the greens until they are wilted and reduced in quantity, about 2 minutes. Mix in garlic, soy sauce, rice wine vinegar, sake, and sugar.
Bring the mixture to a boil, stir until sugar has dissolved, and cover the skillet. Reduce heat to a simmer, and cook until the greens are tender, 10 to 15 minutes. If a thicker sauce is desired, remove greens with a slotted spoon, and cook the liquid down to desired thickness; return greens to the skillet, toss in the pan juices, and sprinkle with toasted sesame seeds.