Shred the cabbage finely, coarsely grate the carrot and thinly slice the mushrooms, removing the tougher stems. Peel the outer layer from the green onions then thinly slice the white and light green part. Have the crushed garlic and grated ginger ready. Combine the soy, sake and mirin for the sauce.
Warm a wok or wide saute pan over a medium-high heat then once warm, add the oil then add the pork into the oil, pressing into a relatively thin layer. Leave it to get a good sear then flip it over to sear the other side.
Break up the meat with a spatula then add the green onion, garlic and ginger (if using), cook briefly so they are aromatic but not burning, then add the cabbage and carrot. Cook, stirring now and then, for around 2 - 3 minutes until the vegetables are starting to soften. Add the shitake mushrooms and cook a minute or two more.
Add the noodles to the wok/pan, separating them as you add as best you can. Mix through briefly then pour over the soy-sake-mirin sauce. Use tongs to toss the noodles, meat and vegetables so they become coated in the sauce, particularly the noodles. After a couple minutes, the sauce will be largely absorbed. Add the sesame oil, toss gently to mix through then remove from heat.
Divide between plates to serve and top with toasted sesame seeds, some finely cut green part of the green onions and thinly sliced pickled ginger (or none/other garnishes to taste).