In a large pot, heat 3 tablespoons oil over high until hot and shimmering. Add onion and garlic, and sauté until golden, about 4 minutes.

Stir in tomato paste, cumin, 1/4 teaspoons each salt and black pepper and the chili powder, and sauté for 2 minutes longer.

Add broth, 2 cups water, lentils and carrot. Bring to a simmer, then partly 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. The 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.