In a large pot, heat 2 tbsp. oil over medium. Add the onion and garlic and cook, stirring often, until the onion is translucent, about 3 minutes. Add the carrots and cumin and cook, stirring often, until fragrant, about 2 minutes. Add the stock and lentils; season with salt and pepper and bring to a boil. Reduce the heat to medium and cook, stirring occasionally, until the lentils are tender, about 30 minutes.
Meanwhile, in a food processor, puree the feta and 1 tbsp. oil until smooth and fluffy, about 2 minutes. Transfer to a small bowl and drizzle with the remaining 1 tbsp. oil. Rinse out the food processor bowl.
In the food processor, puree 2 cups of the soup. Return to the pot and season. Divide the soup among bowls and top with the parsley. Serve with the pita and the whipped feta.