Place the dried porcini mushrooms in large bowl with 6 cups of hot water. Whisk in the bouillon cubes or powder until combined. Set aside for 15 to 20 minutes so the dried mushrooms can rehydrate in the broth.
Once the dried mushrooms are rehydrated, remove them from the broth, and roughly chop. Reserve the broth.
Meanwhile, heat the olive oil in a large Dutch oven or heavy-bottom pot over medium heat. Once the oil is hot, add the mixed and rehydrated mushrooms and season with salt and pepper.
Cook, stirring often, until the mushrooms release most of their moisture – they should cook down quite a bit, 10 to 15 minutes.
Add the onion, carrots, and celery and continue to cook until the onion is translucent, 3 to 5 minutes.
Next, add the garlic, parsley, thyme, sage and garlic powder, and continue to cook until the garlic is fragrant, another 1 to 2 minutes.
Sprinkle in the flour and mix to thoroughly to combine. Cook, while stirring, for 2 to 3 more minutes.
Pour in the wine and simmer until most of it cooks out, 3 to 5 minutes.
Mix in the wild rice and reserved broth. Increase the heat and bring the mixture to a light boil.
Reduce the heat to low, cover and simmer until the rice is tender, 35 to 45 minutes.
Pour in the non-dairy milk and simmer, uncovered, another 15 minutes. Taste and adjust seasonings if necessary. Serve immediately with vegan parmesan and fresh parsley and enjoy!