Prepare the vegetables: Finely chop the onion, mince the garlic, slice the cremini mushrooms, and cut the asparagus into 1-inch pieces, trimming off any woody ends.
Sauté the vegetables: Heat the olive oil in a large pot over medium heat. Add the onion, mushrooms, and asparagus and cook for 4–5 minutes. Stir in the garlic and green curry paste, cook for 30–60 seconds
Simmer the soup: Pour in the vegetable stock and bring to a gentle simmer. Cook covered for 10–12 minutes, until the asparagus is tender.
Blend the soup: Remove from heat and blend the soup until smooth using an immersion blender or carefully transfer to a countertop blender.
Add coconut milk: Return the soup to low heat and stir in the coconut milk. Warm gently without boiling. Season with salt and pepper to taste, then stir in the lime juice just before serving.