Combine 2 cups of the chicken stock and one-third of the potatoes in a small saucepan. Bring to a boil, and then reduce to a simmer until fork-tender, 15 to 18 minutes. Stir in the mustard to combine, and then blend to a smooth puree using an immersion or regular blender.
Meanwhile, cook the bacon in a large Dutch oven or stock pot over medium heat until crispy and most of the fat has been rendered, 12 to 15 minutes, and then transfer to a paper-towel-lined plate to drain. Pour out the bacon fat, reserving 3 tablespoons in the pot.
Turn the heat up to medium-high and add the carrots. Sprinkle with salt and pepper and cook for 3 minutes, and then add the remaining potatoes, celery, bay leaves, leeks and thyme and season with salt and pepper. Cook until the leeks are soft, 4 minutes, and then pour in the beer and bring to a boil until the beer has cooked down to about 2 tablespoons, 2 to 4 minutes. Pour in the remaining chicken stock and the reserved potato puree. Stir to combine and bring the mixture to a boil. Reduce to a simmer and cook uncovered until the vegetables are just tender, 6 to 8 minutes. Season with salt and pepper.
To serve, ladle the soup into bowls. Crumble the reserved bacon on top and garnish with the chives.
Recipe courtesy of Susan Vu for Cooking Channel