Italian Lentil and Chanterelle Soup

Name: Italian Lentil and Chanterelle Soup
Ingredients: 1 small yellow onion; 1 medium stalk celery; 2 small carrots; 1/4 cup olive oil, plus more for drizzling; 1 bay leaf; 2 cups dried brown or French Puy lentils (about 14 ounces); 1/2 cup dry white wine; 2 (32-ounce) cartons low-sodium vegetable broth (8 cups), divided; 1 tablespoon double-concentrated tomato paste (from a tube); 8 ounces fresh chanterelle mushrooms; 1 1/2 ounces Parmesan cheese, grated (generous 1/3 cup); 6 to 8 sprigs fresh parsley; 2 tablespoons unsalted butter; 1/2 teaspoon kosher salt, plus more as needed; Freshly ground black pepper