Preheat the oven to 350 degrees(F).
First, prep the mushrooms, chop them into large chunks. If you are using king oyster mushrooms, I like to shred some and score some to make a meatier texture.
Heat the olive oil on medium high in a large pot that has a lid.
Add the mushrooms, season with a few pinches of salt and pepper, and sauté them, reducing heat as needed, until they have released their liquids and are starting to get a sear on them. About 15 minutes.
Remove the mushrooms from the pot once they have browned and put them in a bowl. Set aside.
Now, add the white wine, sake or lemon juice to the pot and deglaze the bottom of the pot. Scraping any bits of mushroom that got stuck to the bottom.
Then add the vegan butter and heat on medium high. Once it has melted, add the onion, carrots and celery. Season with a few pinches of salt and pepper.
Sauté, reducing heat as needed for 3 to 4 minutes or until the onions are translucent.
While the veggies sauté, whisk together the vegetable broth, miso paste, agave, tomato paste, and rice wine vinegar.
Once the veggies have sautéed for the 3 to 5 minutes, pour the broth you just made into the pot. Stir to combine everything.
Then add the mushrooms back to the pot, stir again, making sure the mushrooms are as submerged as possible.
Cover the pot and roast in the oven for about 1 1/2 hours or until the mushrooms are nice and tender and juicy.
The last 5 minutes of braising the mushrooms is when I add the Thai chilies if you are adding them and the green onions. Stir to combine and put the pot back in the oven for the last 5 minutes. The Thai chilies will make it pretty spicy, so that is definitely optional!
Once the mushrooms only have about 30 minutes left, start the potatoes.
Peel and dice the potatoes then add them to a large pot of room temperature water. Bring the pot to a boil and once it is boiling, boil the potatoes for 15 to 20 minutes or until the potatoes are very tender.
Drain the potatoes once they are very tender.
Now, smash the potatoes with either a potato masher, a ricer or food mill until they are smooth.
Add the vegan butter, hot milk, garlic and a few pinches salt and pepper.
Continue to smash and mash until the potatoes are completely smooth. Taste and adjust seasonings.
Once the mushrooms are done, serve them over a bowl of mashed potatoes.