Heat the olive oil in a large pot over medium heat. Add the chorizo slices and cook for 3 to 4 minutes until they release oil and brown lightly.
Add the onion, carrots, and garlic to the pot. Stir and cook for 5 minutes until the vegetables begin to soften.
Stir in the smoked paprika and chili flakes. Cook for 1 minute to toast the spices.
Add the lentils, chopped tomatoes, and chicken stock. Season with salt and black pepper.
Bring the mixture to a boil, then lower the heat and simmer uncovered for 25 to 30 minutes. Stir occasionally until the lentils are tender.
Ladle into bowls and top with the chopped parsley.