Bring 2 cups of water to a boil.
Place the dried mushrooms (not the button mushrooms) in a medium sized bowl. Pour the boiling water over the top so that they can become reconstituted. Set aside.
In a frying pan heat the oil over medium-high heat.
Saute the onions for about 5 minutes.
Add the chopped button mushrooms and saute for another 5 minutes.
Drain the reconstituted mushrooms.
Add the exotic mushrooms and the button mushroom mixture to a slow cooker.
Add the vegetable broth, white wine, tarragon, salt and pepper.
Cook on low 3 to 4 hours.
Let cool about a half hour.
You may reserve some mushroom pieces for sprinkling over the top as in my photos but you do not need to do this.
Pour the mushroom mixture in a blender and blend until smooth.
Pour into a big pot (or bowl for the microwave) and add the non-dairy milk.
Heat through on low heat on the stove top.
Taste to see if you would like more salt or pepper.