Place leek in an 8- to 10-quart pan. Add onions, carrots, celery, mushrooms, tomatoes, fennel, parsley, thyme, oregano, peppercorns, salt and enough water to cover vegetables (about 2 qt.). Bring to a boil over high heat, then reduce heat and simmer, uncovered, for 2 hours, adding water as needed to keep vegetables barely covered.
Line a colander with a layer of cheesecloth (or use a large, fine wire strainer); set over a large bowl. Pour stock mixture into colander and drain vegetables well; discard vegetables. Reserve stock for use.
For Lentil Soup:
In a large pot, heat 3 tablespoons oil over high heat until hot and shimmering. Add onion and garlic, and sauté until golden, about 4 minutes.
Stir in tomato paste, cumin, salt, black pepper and chili powder or cayenne, and sauté for 2 minutes longer.
Add broth, 2 cups water, lentils and carrot. Bring to a simmer, then partially cover pot and turn heat to medium-low. Simmer until lentils are soft, about 30 minutes. Taste and add salt if necessary.
Using an immersion or regular blender or a food processor, purée half the soup then add it back to pot. Soup should be somewhat chunky.
Reheat soup if necessary, then stir in lemon juice and cilantro. Serve soup drizzled with good olive oil and dusted lightly with chili powder if desired.