Melt the butter in a large pot over medium heat.
Add the onion, bay leaves, and thyme. Cook for 6 to 8 minutes, stirring occasionally, until the onion is soft and translucent.
Add the garlic and cook for 30 seconds, until fragrant.
Stir in the chopped asparagus stalks and cook for another 2 to 3 minutes.
Pour in the chicken stock and bring to a gentle simmer.
Cover and cook for 12 to 15 minutes, or until the asparagus is very tender.
Meanwhile, blanch the reserved asparagus tips in boiling water for 1 minute, then immediately transfer them to an ice bath to keep their bright green color. Drain and set aside.
Remove and discard the bay leaves.