3 medium (2½ pounds) white potatoes, peeled and cut into small dice
4 cups low sodium chicken or vegetable broth
½ cup half-and-half or heavy cream
3 tablespoons vegetable or other neutral-flavored oil
Trim about ½ inch from the tops of the leeks and discard. Using a sharp paring knife, cut halfway through the leeks lengthwise until you reach the center (leeks will still be intact). Run the leeks under cold water, exposing each layer to remove any sand. Thinly slice the leeks, keeping the white and pale green parts separate from the darker green part.
Melt the butter in a large saucepan over medium heat. Add the white and pale parts of of the chopped leeks and cook, stirring, until slightly softened, about 5 minutes. Add the garlic, salt, white pepper, and nutmeg and cook, stirring, until fragrant, 2 minutes. Add the potatoes and cook, stirring often, until the leeks are softened but the potatoes are still tender-firm, about 10 minutes. Add the broth and bring to a boil over medium-high heat. Reduce the heat to low, cover, and simmer until the potatoes soften, 30 minutes.
Using an immersion blender or a blender, blend the soup on medium until thick, creamy, and relatively smooth, 2 minutes. Stir in the half-and-half.
Make the crispy leek topping: While the soup is cooking, heat the vegetable oil over medium-high heat in a 9- or 10-inch skillet. Pat the reserved dark green chopped leeks dry with paper towels and add them to the hot oil. Cook, stirring, until crisped and deeply browned, about 5 minutes. Transfer to a paper towel-lined plate with a slotted spoon and season with salt to taste.
Divide the soup among bowls and top with the crispy leeks.