Wipe the mushrooms clean of any dirt using a damp cloth or paper towel. Cut each mushroom in half, then roughly chop into 1-inch chunks.
Heat a large, heavy-bottomed pot over medium high heat. Add the olive oil and butter and cook until the butter has melted and is slightly foamy.
Add the onion and celery along with 1/2 teaspoon of salt. Sweat the vegetables until the onion is tender and translucent, about 7-8 minutes.
Add the minced garlic and cook until fragrant, about 30 seconds.
Add the chopped mushrooms to the pot along with the thyme springs. Cook, stiring occasionally, until the mushrooms have fully released their liquid, about 10 minutes.
Pour in the stock and bring everything to a low boil. Reduce the heat to low, cover the pot, and simmer for 30 minutes.
Remove the thyme sprigs from the pot. Use an immersion blender, or carefully transfer to a standard blender, and puree the soup to a smooth consistency.
Stir in the coconut cream and cook until the soup has slightly thickened and is heated through, about 5 minutes.
Season the soup with more sea salt and black pepper to taste. Ladle it into bowls and enjoy.