Jens “Improved” Chicken Liver Ragu

Name: Jen’s “Improved” Chicken Liver Ragu
Ingredients: 1/2 cup dried porcini mushrooms + 1 cup boiling hot water; 3 tablespoons extra virgin olive oil, divided; 3 ounces pancetta, finely chopped; 1 cup roughly chopped onion; 1/2 cup roughly chopped carrot; Kosher salt; 8 ounces chicken livers, trimmed and finely chopped; 1 tablespoon double-concentrated tomato paste; 1 ounce Italian (red/sweet) vermouth; 1 ounce dry red wine; 6 whole peeled San Marzano tomatoes (fresh or canned, about 1 cup); 4 large fresh sage leaves, chiffonade (about 1 tablespoon); 1/2 cup cup freshly grated Parmagiano Reggiano, plus additional for serving