Bring a medium nonstick pot to medium-high heat on the stovetop. Add just a bit of water to prevent sticking, and add your onion. Allow to sauté for 3 minutes, stirring occasionally and adding small amounts of water as needed to prevent sticking.
Add mushrooms to the pot and continue to sauté for another 5 minutes, stirring occasionally. The mushrooms will start to release moisture after a minute or two, so water is not usually needed at this point. However, if you have issues with the mushrooms sticking, either stir more frequently or add just a bit of water.
Add vegetable broth, dill, smoked paprika, and tamari to the pot. Bring to a simmer, then allow to simmer for 10 minutes.
In a separate bowl, whisk together flour and cashew milk (when you are done there should not be any lumps of flour and the mixture should be smooth).
Add the milk & flour mixture to the soup. Stir to combine. Place a lid on the pot and allow to simmer 10 more minutes while covered.
Remove the lid from the pot. Add coconut yogurt, lemon juice, parsley, cayenne, and salt. Allow to cook 5 more minutes (uncovered), or until everything is warmed through.
Serve and top with additional coconut yogurt and/or parsley, if desired. Enjoy!