In a large bowl, combine the sausage ingredients and let stand for 15 minutes.
In a medium size 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, 20-22 minutes. Drain and discard the bay leaves and onion.
Meanwhile, in a medium size soup pot, heat 3 tablespoons of the EVOO, a few turns of the pan, over medium heat. Using a food processor, pulse the vegetables, parsley stems and rosemary leaves until chopped; transfer to a pot. Season, cover and let ingredients sweat in the EVOO, 6-8 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 heat. Cook the sausage until brown and crumbly, about 5-7 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 cheese.