Heat olive oil in a large stockpot over medium heat and sauté the onion, carrot, and potato for 5-7 minutes until softened.
Add the tomato paste, cumin, and dried mint, stirring for 1 minute until fragrant.
Incorporate the rinsed red lentils and the broth into the pot.
Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 20 to 25 minutes until the lentils are completely soft.
Remove from heat and process the soup with an immersion blender until smooth and creamy.
Season with salt and black pepper to taste.
In a small skillet, melt the butter over medium heat and stir in the Aleppo pepper until the butter turns red and foams.
Ladle the soup into bowls, drizzle with the chili butter, and serve immediately with lemon wedges.