Melt the vegan butter in a large pot over medium heat, then add the mushrooms. After a few minutes, the mushrooms will begin to release their juices. Continue cooking them and stirring occasionally, until most of the liquid has evaporated, about 15 minutes.
Stir in the onion and cook it with the mushrooms until it starts to soften, about 5 minutes, stirring occasionally.
Sprinkle in the flour and paprika, then stir well to coat the mushrooms. Cook the mixture for 1 minute, stirring constantly.
Add 3 cups of the broth, stirring in just a bit at a time, until all has been added and there are no lumps from the flour. Raise the heat and bring the liquid to a boil, then reduce the heat and let the soup simmer for 15 minutes, until the mushrooms are very tender and the broth has reduced slightly.
While the soup simmers, add the remaining 2 cups of broth to a high-powered blender, along with the cashews. Blend until smooth and milky.
Stir the cashew mixture into the soup and continue simmering for 1 to 2 minutes, until heated through.
Remove the pot from heat. Stir in the lemon juice and soy sauce. Season the soup with salt and pepper to taste, then stir in the dill and parsley.
Ladle the soup into bowls and top each one with a dollop of vegan sour cream or cashew cream and a sprinkle of fresh dill and parsley. Serve.