Reindeer Wurst in Lentil Soup

Name: Reindeer Wurst in Lentil Soup
Ingredients: 1 tablespoon olive oil; 1 pound reindeer sausage (kielbasa can be substituted); 1 large onion, diced; 3 cloves garlic, lightly crushed with the side of a knife blade, then minced; 3 large sprigs fresh thyme, leaves stripped from the stems; 8 cups water; 1 tablespoon balsamic vinegar; 3 large carrots, peeled and diced; 2 cups lentils, picked over to remove any stones or impurities and rinsed; Salt and freshly ground black pepper; 1/8 cup extra-virgin olive oil