Cook onion in EVOO with 1/2 teaspoon salt in a medium heavy saucepan over medium heat, stirring occasionally, until softened, about 8 minutes.
Add garlic, cumin and cook, stirring, 1 minute more. Add lentils, broth, water, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Bring to a boil and immediately simmer, partially covered, stirring occasionally, until lentils are very soft and falling apart, about 30 to 45 minutes.
Stir in parsley and season with sea salt and pepper.