1. Open the can of asparagus and drain off the liquid. Rinse the asparagus gently under cold water. Separate the tips from the stalks, setting the tips aside; they will be added at the end.
2. Place the asparagus stalks in a medium saucepan with the 2 cups (480 ml) cold water. Bring to a boil over medium-high heat and boil for 5 minutes, until the stalks are softened and the water is lightly colored. Drain and discard the cooking water.
3. Return the drained stalks to the saucepan. Add the White Stock and the slice of onion. Bring to a boil, then reduce heat to maintain a steady boil and cook for 30 minutes, until the stalks are very tender and the stock is well flavored.
4. Remove from heat. Pass the soup through a fine-mesh sieve into a clean heavy saucepan, pressing firmly on the solids to extract all liquid; discard the solids. The strained liquid should be smooth and pale green.
5. Prepare a beurre manie (a technique in which equal parts raw butter and flour are worked together into a paste to thicken a liquid without lumping): mash the 1/4 cup (55 g) butter and 1/4 cup (30 g) flour together with a fork until a smooth paste forms.
6. Scald the milk (a technique in which milk is heated just below a simmer, to approximately 180°F / 82°C, until small bubbles appear around the edges of the pan but no rolling boil occurs). Keep warm.
7. Return the strained soup base to medium heat. Whisk in the beurre manie a small piece at a time, stirring constantly, until fully incorporated. Continue to cook, stirring, for 3 to 5 minutes, until the soup thickens enough to lightly coat the back of a spoon and no raw-flour taste remains.
8. Stir in the scalded milk, reserved asparagus tips, salt, and pepper. Heat gently over medium-low heat for 2 to 3 minutes, until the tips are warmed through and the soup is steaming and uniform in consistency. Do not boil after the milk is added. Taste and adjust seasoning before serving.
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