Rinse lentils. Place lentils, chorizo, whole garlic cloves, carrots and potatoes in a large pot. Fill pot with water until ingredients are submerged by two inches.
Bring to a boil, then lower to a simmer. Let cook uncovered, stirring occasionally.
Sauté onions in a pan with olive oil until slightly browned, then add paprika. Add onions to the pot of lentils. Cook for 45 minutes.
Remove the cloves of garlic, squeeze garlic from its skin and mash. Return to the pot. Salt to taste.