In a 5-quart soup pot, bring broth, water, lentils, onion, garlic, cumin, and cayenne pepper to a boil; reduce heat to low, cover, and simmer 25 minutes.
Meanwhile, heat oil in a large skillet over medium heat. Add chorizo or sausage links and cook 12 to 15 minutes, or until fully cooked. When cool enough to handle, cut chorizo into slices. Add to soup, along with spinach, and cook 3 to 4 minutes longer, until spinach is wilted.