In a large pot, heat oil and sauté onion and leeks over a low flame until soft and translucent, about 10–15 minutes. Add garlic and sauté another two to three minutes until fragrant. While onions are sautéing, slice asparagus into one-inch (two-and-a-half-centimeter) pieces, reserving the stems for later.

Add asparagus, potatoes, water, and soup mix to the pot and bring to a boil. Lower heat and simmer gently for 45 minutes to one hour, or until the vegetables are soft.

Add wine and spices and blend soup until smooth and creamy. Add the asparagus tips and cook for an additional 15–20 minutes until tender. Top with soup croutons before serving, if desired.