Clean the leeks: Trim off the dark green tops and the root ends. Halve each leek lengthwise, slice into 1/4-inch half moons, then drop them into a big bowl of cold water and swish with your hands. The grit sinks. Lift the leeks out of the water rather than pouring the bowl into a colander.

Sweat the leeks: Melt the butter in a large pot or Dutch oven over medium heat. Add the leeks and cook 10 minutes, stirring every couple of minutes, until they're completely limp and sweet. Turn the heat down if you see any browning at the edges.

Add the garlic: Stir in the garlic and cook 1 minute, just until it smells good.

Simmer the potatoes: Add the potatoes, chicken broth, bay leaves, thyme sprigs, salt, and pepper. Bring to a boil, then cover, drop the heat to low, and simmer 20 minutes, until a potato piece falls apart with no resistance when you press it against the side of the pot.

Blend it smooth: Fish out the bay leaves and the thyme stems. Purée with an immersion blender in short bursts, moving it around the pot, until the soup is smooth. Stop as soon as it gets there.

Stir in the cream: Pour in the heavy cream and simmer uncovered 3-4 minutes, until the soup is steaming and slightly thickened. Taste and add salt, because cream mutes it.

Serve: Ladle into bowls and scatter the chopped chives over the top.