Heat a large wok or skillet over medium.
Once hot, melt the vegan butter.
Add in the white parts of the green onion and cook for 1 minute. Add in the minced garlic and cook until aromatic.
Add in the mushrooms into the wok or skillet and mix with the onions, garlic, and butter.
Leave the mushrooms untouched for 2-3 minutes over medium high heat to allow to lightly brown before mixing and allowing the other sides of the mushrooms to lightly brown. Cooking the mushrooms in high heat is essential so they don’t release much water and turn soggy when cooked slowly on low heat.
Once the mushrooms have a nice sear and lightly brown sides, add in the sake or mirin (if using) and then turn up to heat to allow for the alcohol to evaporate.
Pour in the plant-based milk of your choice (or cream, see notes), miso paste, and soy sauces.
Allow the sauce to come to a boil then lower the heat.
Add in the udon or noodles of your choice.
Mix the noodles to coat in the sauce. Add freshly ground pepper.
In a small bowl, mix together the corn starch and water to create a slurry.
Over medium low heat, pour the slurry over the noodles. Mix the noodles and allow the sauce to thicken from the starch.
Taste the sauce and noodles and season with more soy sauce or salt, to taste, if needed.
Turn off the heat. Do note that the sauce will continue to thicken once the heat is turned off.
Mix in the green parts of the green onion into the noodles or use these as garnish.
Serve and enjoy while hot.