In a large pot, over medium-high heat, cook the bacon (1/2 pound) until crisp. Transfer to a paper towel-lined plate. Add celery (1 rib), onion (1/2 cup), jalapeno (1 large), garlic (4 cloves), and thyme (1 tablespoon) to the pot and saute over medium heat until vegetables are soft about 8 minutes.
Melt the butter (4 tablespoons) in a small pot. Add the flour (1/4 cup)and cook over medium heat, whisking constantly, until lightly browned about 1-2 minutes. Pour in half of the beer and whisk until reduced by half, about 1 minute. Pour in chicken broth (2 1/4 cups) and bring soup to a simmer.
Pour the roux into the soup pot and whisk until incorporated. Bring to a boil, stirring frequently, then immediately reduce to a simmer. Cook, stirring occasionally until soup thickens, about 8 minutes.
Stir in heavy cream (1 cup), 3 cheeses, and the remaining beer and simmer, stirring occasionally, until thick and creamy, about 5 minutes. Add the cooked bacon and season with salt and pepper.