Make soup: In a medium pot, melt 2 tablespoons of the butter over medium-high heat. Add oil and mushrooms and season with salt. Cook, stirring occasionally, until mushrooms are tender and any liquid they've given off has evaporated, about 5 minutes. Transfer mushrooms to a plate.
Melt remaining 2 tablespoons of butter over medium heat. Add onion and carrot and cook, stirring occasionally, until onions are softened, about 3 minutes. Add garlic and cook, stirring, until lightly toasted, about 2 minutes. Stir in miso.
Add wine to pot and increase heat to medium-high. Bring to a boil and cook until wine evaporates, about 3 minutes.
Add water and potatoes to pot. (There should be just enough water to cover potatoes; add a little more as needed.) Season with salt and bring to a boil. Cover pot, reduce heat to medium, and simmer until potatoes and carrots are tender, about 10 minutes.
Meanwhile, make “cream” sauce: In a small saucepan, cover russet potatoes with at least 1 inch of water. Season with 1 teaspoon salt and place over medium-high heat. Bring to a boil, reduce heat to medium, and cook until potatoes are very tender, about 7 minutes. Drain.
Transfer cooked potatoes to a blender and add almond milk. Puree until a smooth.
When vegetables are tender, uncover the pot, add “cream,” and stir to combine; season with salt and pepper.
Just before serving, stir mushrooms back into pot to warm through. Ladle soup into bowls and top with parsley and oyster crackers.