Ingredients

• 1/2 cup (1 stick) unsalted butter
• 6 large leeks, white and pale-green parts only, halved lengthwise, thinly sliced crosswise
• 1 small onion, thinly sliced
• 5 garlic cloves, thinly sliced
• Kosher salt
• 2 cups whole milk, divided
• 1 cup heavy cream, divided 1 cup plain whole-milk yogurt, divided
• Freshly ground black pepper
• 1 russet potato, peeled, cut into thin matchsticks Vegetable oil (for frying; about 4 cups)
• 1/4 cup fresh flat-leaf parsley leaves
• 1 sprig rosemary
• Kosher salt
• Flaky sea salt (such as Maldon)
• A deep-fry thermometer

Instructions

1. Melt butter in a large heavy pot over medium heat. Add leeks, onion, and garlic and season with salt. Cook, stirring often, until vegetables begin to soften, 5-7 minutes. Add 1 cup water and cook, stirring occasionally, until vegetables are very soft, 25-30 minutes. Let cool slightly, then transfer half of leek mixture to a blender and add half of milk, cream, and yogurt. Purée until very smooth; pour into a large bowl. Repeat with remaining leek mixture, milk, cream, and yogurt.
2. Return soup to pot and heat over medium, adding water by ¼-cupfuls, until soup is thick enough to hold potatoes without sinking but thin enough that a spoon dragged across the top doesn't leave a trail.
3. Season with salt and pepper.
4. Rinse potato in a colander under cold water until water runs clear; pat completely dry.
5. Fit a medium saucepan with thermometer; pour in oil to measure 2". Heat over medium-high until thermometer registers 350°F. Working in batches and returning oil to 350°F between batches, add potato by the handful and fry, turning occasionally, until golden and crisp, about 2 minutes. Using a spider or slotted spoon, transfer potato to paper towels to drain. Fry parsley and rosemary until parsley is translucent, about 15 seconds. Add to potato and let cool; season with kosher salt. Serve soup topped with a nest of potatoes and herbs and seasoned with sea salt.