Add onion and celery, and garlic to the pot, reducing heat to medium-low. Cook, stirring occasionally until softened, about 5 minutes
Add mustard seeds, bay leaf, thyme leaves, and salt, stirring to coat, about 1 minute
Add 6 cups of the stock, the potatoes, asparagus stems, and lemon juice. Bring to a boil, then reduce heat and simmer, covered, 20 minutes.
Meanwhile, in another pot, add the remaining two cups of stock, plus the woody end of the asparagus stems. Bring to a boil, then reduce heat to medium and allow to simmer while the soup does, 20 minutes
Using a sieve, strain the cooking liquid from the woody ends into the soup, and discard the ends.
Using an immersion blender, puree the soup to a smooth consistency.
Add asparagus tips to the soup and simmer a further 5 minutes
Stir in dill, remove from heat, and serve topped with croutons
If you don't have an immersion blender, you can use a blender to puree the soup in batches. Just be careful to allow the steam from the hot soup to escape from the blender.