In a medium heavy-duty soup pot, heat 3 tablespoons of olive oil over medium-high heat. Add the mushrooms and shallots and cook, stirring occasionally, until they are starting to caramelize, about 10 minutes.
Add the bourbon, thyme, ½ teaspoon of salt, and ¼ teaspoon of pepper; stir well and scrape off any browned bits from the bottom of the pot.
Add 3½ cups of water and bring to a boil. Reduce the heat to a simmer and cook for 25-30 minutes, or until the mushrooms are tender. Remove from the heat and let cool slightly.
To make the garnish, sauté the additional 4 ounces of mushrooms in the remaining tablespoon of olive oil until nicely browned. Set aside.
Puree the soup with an immersion blender. Add the coconut milk and return to a simmer. Heat the soup through for a few minutes. Adjust the seasoning, ladle into bowls, and serve immediately, garnished with the sautéed mushrooms and fresh herbs, if using.