In a medium pot, add canola oil, onion, Portobello, and Shiitake mushrooms.
Cook on medium heat for 10 minutes, stirring.
Save ¼ cup of mushroom mix for later to top the soup bowls. Set aside in a small bowl.
To the pot with the remaining mushroom mix, add water, coconut milk, rice, bay leaf, white pepper, miso paste, soy sauce, and bring to boil.
Then lower the heat and let the soup simmer for 15 minutes, covered.
Uncover, add fresh dill, garlic, pine nuts, and nutritional yeast. Simmer for 2 more minutes.
Remove pot from heat and puree the mixture, either with an immersion blender or a food processor.
Once pureed, season with any additional salt to taste.
Serve topped with mushrooms you saved in a small bowl.