Start cooking the rice first, so it is ready when the stir-fry is. (You may want to give the rice a head start of 20 minutes or so, depending on your choice of rice).
Using your hands or a wooden spoon, work ginger and garlic into sausage in a medium bowl.
Heat 2 Tbsp. oil in a large wok or skillet, over medium-high.
Cook sausage mixture, breaking up with a wooden spoon, until browned, crisp, and cooked through, 6–8 minutes.
Using a slotted spoon, transfer sausage mixture to a clean bowl, keeping the fat in the skillet.
Increase heat to high and cook mushrooms in the fat in the skillet, tossing often, until browned and starting to release their juices, about 4 minutes (if skillet looks dry at any point, add a bit more oil).
Add half of cabbage and cook, tossing often, until cabbage is wilted and tender, about 4 minutes.
Add vinegar and soy sauce and cook, tossing, until liquid is mostly reduced and skillet is dry in spots, about 2 minutes.
Remove skillet from heat and mix chives, sausage, and remaining cabbage into stir-fry. Drizzle with sesame oil and sprinkle with sesame seeds.
Serve stir-fry over freshly cooked rice, and drizzle with sauce of your choice.