Combine the mushrooms, leeks, butter, 1/2 teaspoon salt and 1/4 teaspoon pepper in large Dutch oven. Cover and cook over medium-low heat, stirring occasionally until the mushrooms are softened, 8 to 10 minutes. Uncover, increase the heat to medium-high, and continue to cook, stirring occasionally, until the mushrooms are well-browned, 8 to 12 minutes longer. Transfer 2/3 cup of the mushroom mixture to a cutting board, chop fine and set aside.

Stir the garlic and thyme into the pot and cook until fragrant, about 30 seconds. Stir in the broth and Madeira, bring to a simmer, and cook until the mushrooms and leeks are completely tender, about 20 minutes.

Working in 2 batches, process the soup in a blender until completely smooth, 2 to 3 minutes.

Return the soup to the pot. Stir in the chopped mushroom mixture, half-and-half and lemon juice and cook until heated through. Season with salt and pepper to taste and serve, drizzling individual portions with additional Madeira.