Slice the chorizo into bite-sized pieces that can fit in a spoon.
Wash and peel the potatoes and onions. Cut them up into coarse, bite-sized pieces. Peel the onions and garlic. Mince finely and set aside.
The cooking
Pour olive oil into a large pot and heat over medium heat. Add the potatoes, carrots, and onions and sauté for 4-5 minutes. Add the garlic last, some 20-30 seconds before the rest of the vegetables are done sautéing.
Add the tomato puree, tomato paste, lentils, and chorizo. Season with salt and paprika and liven up a dash or two of vinegar. Fill up with water and cover the pot, leaving the lid slightly ajar. Let boil for 45 minutes to 1 hour.
Notes
If you like your lentil stew extra savory, ditch the sea salt and sweet paprika and replace with 1 cup beef stock and smoked paprika.