Heat 2 tablespoons extra virgin olive oil in a large pot or Dutch oven over medium heat. Add 1 medium onion, 2 medium carrots, and 2 ribs celery (all chopped) and cook for 7 to 8 minutes, stirring occasionally, until softened.
Stir in 3 cloves garlic (grated), 2 tablespoons tomato paste, 2 bay leaves, and 1 teaspoon dried thyme. Cook for 1 minute, stirring often.
Rinse 1 cup French green lentils well and cut 2 medium potatoes into small bite-size pieces, about ¾-inch cubes. Add the lentils, potatoes, 5 cups vegetable broth, ½ teaspoon salt, and ¼ teaspoon black pepper. Stir and bring to a boil.
Reduce the heat and simmer gently, partially covered, for 30 to 35 minutes, stirring a couple of times. The soup is ready when the lentils are tender and the potatoes are easily pierced with a fork. If it gets too thick, add a splash of broth or water.
Remove the bay leaves and stir in 1½ tablespoons red wine vinegar. Taste and add more salt, pepper, or vinegar if needed. Serve hot with optional chopped parsley and a drizzle of olive oil.
