Heat a 4½-quart Dutch oven or heavy skillet over medium-high heat. Add bacon and cook until crisp, about 8 minutes. Transfer to a paper towel-lined plate to drain.

Discard all but 2 tablespoons of the fat in the pot. Reduce the heat to medium and add the butter. Add the onion, apple, carrot, and celery. Cover and cook, stirring occasionally, for about 10 minutes.

Add the garlic and cook for 1 minute. Add the dry mustard, paprika, and gluten-free flour. Cook, stirring occasionally, for 3-4 minutes. Add the gluten-free ale and cook, stirring constantly, for 2-3 minutes. Add the Worcestershire sauce, milk, and broth. Increase heat to medium-high and bring to a simmer for 2 more minutes. Reduce the heat to medium-low and simmer for another 10-12 minutes.

Remove the pot from the heat and puree the soup with an immersion blender until smooth.

Set the pot over medium-low heat and add the cheese by the handful, stirring constantly. Do not allow the soup to boil. Season the soup with salt and pepper to taste. Ladle into bowls. Top each bowl of soup with reserved bacon pieces and chives for garnish. Enjoy with slices of your favorite gluten-free baguette.