Chop all vegetables, including the rehydrated or fresh mushrooms, into small pieces.
In a large pot, heat olive oil over medium heat.
Add diced onion, carrot, and celery and cook until the onion is translucent.
Add minced garlic and sauté for an additional minute until fragrant.
Add mushrooms, potato, thyme, rosemary, smoked paprika, vegetable broth, and bay leaf to the pot.
Bring the mixture to a boil, then reduce heat to simmer.
Cook until the vegetables are tender.
Remove the bay leaf from the pot.
Using an immersion blender or transferring the soup to a blender, puree the soup until smooth.
Return the soup to the pot and stir in the coconut milk.
Simmer for an additional 5-10 minutes, until warm.
Taste the soup and add salt and pepper, adjusting to your liking.
Ladle the soup into bowls, and garnish with fresh parsley and croutons, if desired.
