White Bean Soup with Chive Oil

Name: White Bean Soup with Chive Oil
Ingredients: 2 cups dried Great Northern or other small white beans, rinsed and picked over; 3 tablespoons olive oil; 1 large onion, chopped; 1 cup chopped leeks (white and pale green parts only); 1 large tomato, halved, seeded, and chopped; 1/2 cup chopped carrots; 1/2 cup chopped celery; 8 garlic cloves, chopped; 11 cups homemade chicken stock or canned low-salt chicken broth, or more as needed; 1 tablespoon chopped fresh thyme; 1 tablespoon chopped fresh rosemary; 1/2 cup half-and-half; Salt and freshly ground black pepper; Chive Oil for drizzling