1. Preheat the oven to 375 F degrees. Line a rimmed baking sheet with parchment paper or aluminum foil. (Or coat with a good layer of cooking spray.)
2. Arrange the asparagus, onion halves and garlic cloves on the baking sheet, and brush with olive oil. Sprinkle with some salt and pepper, and then bake for about 45 minutes. Turn the onions if they start getting overly dark on the bottom. Check on the garlic as well, once the cloves are golden and oozy inside (probably after about 20 minutes), pull them from the oven.
3. Peel the garlic, and chop the asparagus into smaller (about 2″) pieces. Reserve some of the asparagus heads for garnish. Then add the asparagus, onions, and garlic into a medium-sized saucepan, and add chicken broth and thyme.

An immersion blender:

1. Just place it directly in the pot so that it is completely submerged, and then blend the soup until it is smooth.

A regular blender or food processor:

1. You’ll probably need to do this in batches – just take a few cups and blend until smooth. (Also, be careful not to overfill the blender or food processor!)
2. Be careful working with warm/hot liquids! Once the soup is pureed, return the saucepan to the stove and bring soup to a boil over medium-high heat. Then lower heat to medium, and stir in half and half (or cream) and vermouth. Season with additional salt and pepper, and a dash of lemon juice if you’d like. Garnish with asparagus heads.