Heat coconut oil in a large pot over medium heat. Add carrots, celery, onion, garlic, and star anise; cook and stir until onion is translucent, 5 to 7 minutes. Pour in vegetable broth; bring to a boil.
Stir carrot tops, basil, and tarragon into the pot; simmer until wilted, about 5 minutes. Season with salt and pepper. Discard star anise before serving.