1.In a large stockpot, combine the water or stock, asparagus ends and separated leek greens. Heat over low heat and allow to simmer while you prepare the rest of the ingredients.
2.In a medium saute pan, heat the butter and oil. Add the leek 'whites', onion and rice and cook until the onion begins to color (about 8 minutes). Add 1 cup of the warm stock and cook 10 more minutes.
3.Strain the stock of the asparagus and leek ends and return to the stockpot. Add the contents of the saute pan to the strained stock along with the asparagus middles and partially cover the pot. Cook 12 more minutes.
4.Transfer soup to a food processor and puree. Strain this back into the stockpot. Season and add salt, pepper and lemon juice to taste. Meanwhile, drop the asparagus tips into boiling salted water and cook until tender (about 4 minutes). Serve the soup with a few asparagus tips on top for garnish.
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