1. Melt fat in a Dutch oven over medium-low heat.
Add mushrooms, leeks, ½ teaspoon sea salt, and ¼ teaspoon pepper, cover, and cook until mushrooms are softened and wet, 8 to 10 minutes. Uncover, increase heat to medium-high, and cook, stirring occasionally, until mushrooms are dry and well browned, 8 to 12 minutes.
Transfer ⅔ cup of mushroom mixture to a cutting board and chop finely; set aside.
2.
Stir garlic and thyme into pot and cook until fragrant, about 30 seconds.
Stir in broth and Madeira, bring to a simmer, and cook until mushrooms and leeks are completely tender, about 20 minutes.
Cool, before proceeding to the next step.
3.
Working in batches, process the soup in a blender until it is smooth. Return soup to a clean pot and stir in chopped mushroom mixture, coconut milk, and lemon juice. Reheat soup gently over medium-low heat and season with sea salt and pepper to taste.
Drizzle individual bowls with extra Madeira before serving.