Warm the butter and olive oil in a Dutch oven or heavy-bottomed pot over medium-high heat. The butter should melt and foam gently without turning brown.

Add the chopped onion and cook for about 2 minutes. Stir until it looks translucent and smells sweet rather than sharp.

Stir in the leeks and cook for about 4 to 5 minutes. Let them soften completely while keeping every piece pale and free of browned edges.

Add the diced potatoes, season with salt and pepper, and stir them with the softened alliums for a couple of minutes. The potatoes should be coated in the fragrant butter and oil mixture.

Pour in the chicken broth and bring the pot to a boil. Scrape the bottom as the broth heats so all the softened vegetables are evenly distributed.

Reduce the heat and simmer for 30 minutes. A fork should slide easily through the potatoes when they are ready to puree.

Blend the soup until smooth with an immersion blender, or blend it in batches in a regular blender. Keep the blending gentle and stop once the puree is uniform to avoid overworking the potato starch.

Stir in the heavy cream and return the soup to medium heat for about 5 minutes. The soup should look glossy and lightly thicken enough to cling to the back of a spoon.

Taste the soup, adjust the salt and pepper, and stir in the nutmeg before removing the pot from the heat. The seasoning should taste slightly more pronounced than expected for hot soup because chilling softens it.

Let the soup cool to room temperature, then chill it for at least 1 hour before serving. For the fullest flavor and a more settled texture, chill it overnight.

Finish each serving with chopped chives. The fresh green garnish should add a clean, oniony lift against the pale soup.