Heat the EVOO in a soup pot over medium-high heat. Add the sausage and cook, crumbling with a wooden spoon, until browned. Add the garlic, bay leaves, rosemary, carrots, onions and potatoes and season with salt and pepper. Cook until the vegetables are soft, 7 to 8 minutes. Stir in the tomato paste and cook for 1 minute. Stir in the kale and nutmeg. Add the wine to deglaze the pot, stirring and scraping up any browned bits from the bottom. Stir in the chicken stock and 2 cups water and bring to boil (for thicker soup, use 2 cups less liquid).
Stir in the lentils and cook at a low, bubbly simmer until the lentils are tender, 30 to 35 minutes. Remove the rosemary stems and bay leaves.
Ladle the soup into bowls and top with a drizzle of EVOO and the shaved Pecorino.
The soup can be refrigerated in an airtight container for a make-ahead meal. Reheat over medium heat.