Heat the olive oil in a heavy stockpot over medium heat. Add the onion, celery, and garlic, and sauté for 8 minutes, or until the onion is translucent. Stir in the potato, basil, oregano, and cumin. Add the stock and bring to a simmer over high heat. Decrease the heat to medium low, cover, and simmer, stirring occasionally, for 10 minutes, or until the potato is almost tender. Add the asparagus stalks and simmer for 5 minutes, or until the asparagus is tender and the potato is very tender.
Using a hand-held immersion blender, purée the soup in the pot until smooth. Alternatively, working in batches, purée in a regular blender until smooth. Stir in the tamari, salt, and white pepper. Return the soup to a simmer, then stir in the cilantro.
Meanwhile, cook the reserved asparagus tips in a saucepan of boiling water for 1 minute, or until crisp-tender. Drain, then cut the asparagus tips in half lengthwise.
Ladle the soup into individual bowls. Garnish with the asparagus tips and serve.
The soup and uncooked asparagus tips will keep for 2 days, covered separately and refrigerated.