Chop asparagus into 1/2-inch pieces, reserving 8 of the spear tips.
In a large sauce pan, heat olive oil over low heat. Add onion. celery and carrots and cook for about 3 minutes. Add garlic and cook until fragrant; about 1 minute. Add asparagus, salt and pepper and cook an additional 5 minutes. Add broth, cover and simmer for 20 minutes.