With a sharp knife, cut off roots and the tough dark green part of the leeks. Slice the white and light green part of the leeks into 1/4-inch-thick slices. Place in a colander and rinse well under cold water to remove the dirt. Drain well.
In a large Dutch oven or pot, melt the butter over medium heat. Add the leeks and sauté until tender, about 8 to 10 minutes. Add the garlic and cook for 1 minute.
Add the potatoes, broth, thyme, salt, and pepper. Bring to a boil and turn the heat to low. Cover and simmer for 15 to 20 minutes, until potatoes are fork tender.
Use an immersion blender to blend the soup in the pot. Blend until smooth, but don’t over blend or the soup will get gummy in texture.
Alternatively, you can blend the soup in a large blender. Let the soup cool for a few minutes before blending so it’s not steaming hot.Fill the blender halfway, don’t fill it any fuller or you will have an explosion. Place a towel over the top of the blender. Hold the towel in place with your hand and blend the soup. Pour pureed soup back into the pot. Repeat with remaining soup and return to the pot.
Once the soup is all blended, stir in the heavy cream. Taste and adjust salt and pepper, if necessary. Gently warm over low heat.
To serve, pour the soup into bowls and garnish with fresh chives, if desired.
Notes
If you prefer a chunky potato leek soup, you can use a potato masher instead of an immersion blender or blender to give you a chunkier soup texture.Store leftover soup in the fridge for up to 4 days. Freeze for up to 3 months in a freezer container.