Heat olive oil in a large soup pot over medium heat.
Add onion, garlic, carrots, and potato , season with salt, and sauté until softened (about 5–7 min).
Stir in tomato paste , then add red lentils, broth, cumin, Aleppo pepper/paprika , and coriander (if using).
Bring to a simmer, reduce heat to low, and cook until lentils are soft — about 20 minutes.
Use an immersion blender to puree the soup until smooth and creamy. (Or carefully transfer to a blender in batches.)
Taste and adjust salt/pepper.
Serve with a drizzle of extra olive oil and lemon wedges on the side.