Warm Sausage and Lentil Salad

Name: Warm Sausage and Lentil Salad
Ingredients: 2 tablespoons red wine vinegar; 2 teaspoons Dijon mustard, plus more for serving; 6 tablespoons extra-virgin olive oil, divided, plus more for serving; Kosher salt; Pepper; 2 carrots, finely chopped; 1/2 small fennel bulb, finely chopped; 1 1/4 pounds garlic sausages, preferably French; 1 1/2 cups green lentils, preferably du Puy (10 ounces); 2 shallots, halved; 3 thyme sprigs; 1 bay leaf; 1 cup shelled walnuts (4 ounces); 1/4 cup chopped parsley, plus more for serving