Combine sausage ingredients in a bowl and let stand 15 minutes.
Place lentils in pot with bay, onion and some salt, and cover with water. Bring to a boil and cook until tender but with a bite left to them, 20-22 minutes. Drain and discard the bay and onion.
Meanwhile, heat olive oil, a few turns of the pan, in medium soup pot. Add carrot, onion, celery, parsley stems, rosemary and potato, and season with salt and pepper. Cover to sweat, 6-8 minutes. Add stock and 2 cups water, bring to a boil then reduce heat and simmer.
While soup comes to boil, heat a little oil in nonstick skillet over medium-high heat. Add sausage and crumble and brown, 5-7 minutes. Drain fat and add to the soup along with the lentils. If not serving right away, cool and store then reheat over medium flame.
Serve soup in shallow bowls garnished with parsley and Pecorino.