1. Place potatoes in a medium saucepan with just enough water to cover completely. Bring water to a boil and add 1 teaspoon salt. Reduce heat and simmer gently 10 minutes. Remove from heat and let potatoes sit in water 10 minutes; drain.

2. Meanwhile, whisk together mustard, garlic, 1 teaspoon salt, and egg yolk in a medium bowl to combine. Slowly whisk in oil until mixture is thickened and emulsified. Whisk in lemon juice. Rinse preserved lemons in cold water. Remove and discard any lemon flesh and cut rind into small pieces (you should have 1/4 cup).

3. While potatoes are still slightly warm, cut in half and smear a small dollop of aioli on each cut side. Arrange on a serving platter and garnish with preserved lemons, poppy seeds, and chives.