2 pounds (about 2 bunches) asparagus
5 large stalks (4 ounces) green garlic
1 yellow onion. diced
2 tablespoons olive oil
1 teaspoon salt
1 large potato, peeled and diced
lemon juice, to taste
Fill a pot with 2 quarts of water and bring to a boil. Snap the woody ends of the stems from the asparagus spears and discard; they will naturally break at the right spot. Keep the heads intact and slice the stems. Blanche the asparagus in the simmering water for 1-2 minutes, until bright green and crisp-tender. Strain through a colander and into a large bowl, reserving the asparagus water. Rinse the asparagus under cool water to stop the cooking and set aside.
Trim the root ends from the green garlic. Slice the green garlic (leafy green parts included) crosswise into thin rounds and place the rounds in a large bowl to remove any excess dirt. Drain.
Melt the olive oil in a soup pot or Dutch oven over medium heat. Add the onions and green garlic and sauté until bright green and tender, 5-10 minutes. Add the salt, potato, and enough of the reserved asparagus cooking water to cover the vegetables, 4-6 cups. Bring to a boil, then cover the pot and simmer until the potato is very tender, 10 minutes.
Add the asparagus, reserving several pretty heads for garnish, and puree the soup with an immersion blender, or in batches in a regular blender, thinning with more asparagus water as needed. Stir in the juice of half a lemon, taste for salt, adding more salt or lemon as needed. Garnish with asparagus tips.