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1
Trim the attractive top tips from the asparagus, about 1 to 1 1/2 inches in length.
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2
Cut the woody stem ends from each spear and reserve.
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3
Cut the remaining tender stalks into 1/2-inch pieces.
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4
In a medium pot, bring the stock to a boil.
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5
Add the tough woody stems, lower the heat and simmer to infuse with asparagus flavor, 20 to 30 minutes.
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6
Remove with a slotted spoon and discard, reserving the stock.
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7
Add the decorative tips to the stock and blanch until tender, 1 to 1 1/2 minutes.
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8
Remove with a strainer and refresh in an ice water bath.
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9
Drain on paper towels and reserve for the garnish.
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10
Reserve the stock.
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11
In a medium stockpot, melt the butter over medium-high heat.
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12
When foamy, add the shallots and leeks and cook until tender, about 3 minutes.
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13
Add the garlic and cook until fragrant, about 1 minute.
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14
Add the chopped asparagus stalks, salt, and pepper, and cook, stirring, for 2 minutes.
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15
Add the reserved broth and simmer until the asparagus are very tender, 15 to 20 minutes.
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16
Remove from the heat.
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17
With a hand-immersion blender or in batches in a food processor, puree the soup until smooth.
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18
Adjust the seasoning, to taste.
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19
If serving right away, return to medium heat and add the cream and reserved asparagus tips.
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20
Cook, stirring, until the soup is warmed through, about 3 minutes.
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21
Alternatively, if serving the soup later, do not add the cream and let cool at room temperature (or in an ice water bath).
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22
Cover and refrigerate.
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23
Before serving, add the cream and asparagus tips, and warm the soup gently over medium heat, stirring occasionally.
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24
To serve, place the soup in a soup tureen and sprinkle with cheese.
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25
Ladle into demi-tasse cups or small coffee or tea cups, and serve.
