In a large bowl, combine the sausage ingredients and let stand 15 minutes.
In a medium saucepan, place the lentils with the bay leaves, onion and salt. Cover with 2 inches of water, bring to a boil and cook until tender but with some bite, 20 to 22 minutes. Drain and discard the bay leaves and onion.
Meanwhile, in a medium soup pot, heat 3 tbsp. of the EVOO, a few turns of the pan, over medium heat. Using a food processor, pulse the vegetables, parsley stems and rosemary leaves from sprigs until chopped; transfer to pot. Season, cover and let ingredients sweat in the oil, 6 to 8 minutes. Add the stock and 2 cups water. Bring to a boil, then reduce the heat and simmer until the potatoes are tender, about 12 minutes.
While the potatoes are cooking, heat a little EVOO in a large nonstick skillet over medium-high. Cook the sausage until brown and crumbly, about 5 to 7 minutes. Drain the fat, then stir the sausage into the soup along with the cooked lentils. Serve the soup in shallow bowls and top with the reserved parsley leaves and the pecorino-romano.