Sauté the Onions and Garlic:

In a sizable pot, melt the unsalted butter and olive oil over medium heat. Add the chopped onion and cook until it becomes translucent, which should take about 5 minutes. Incorporate the minced garlic and sauté for an additional 1-2 minutes until it becomes fragrant.

Add the Mushrooms:

Mix in the sliced mushrooms and cook them until they release their moisture and become tender, approximately 8-10 minutes.

Add Broth and Seasoning:

Pour in the vegetable or chicken broth, then add the dried thyme, salt, and black pepper. Bring the mixture to a boil, then lower the heat and let it simmer for around 10 minutes.

Blend the Soup:

For a creamier consistency, utilize an immersion blender to puree the soup to your preferred texture. If you favor a chunkier soup, you may opt to skip this step.

Stir in the Cream:

Add the heavy cream or coconut milk to the pot and stir thoroughly. Heat the soup on low for about 5 minutes, ensuring it does not boil.