Diced bacon into small pieces. Cook in a Dutch oven over medium heat until crispy, about 8 minutes. Scoop out cooked bacon and drain on paper towels. Do not discard bacon drippings.
Add diced celery, onion, garlic, and thyme to bacon drippings and continue to cook over medium heat until softened, about 8 minutes. Do not let the vegetables burn so make sure you stir occasionally. Add half of the beer and reduce by half. Then, add in all the chicken broth and bring to a simmer.
While the broth is heating up, make the roux. In a small skillet, melt butter over medium heat. Add flour to melted butter and whisk together. Continue to whisk until roux turns from yellow to light brown, about 5 minutes. Pour roux into the soup and whisk together. Bring soup back up to a simmer and let the soup thicken for about 10 minutes. Add milk and remaining beer and mix together.
Add cheese to the soup in 1/2-cup bunches, whisking after every addition. This prevents clumping and helps the cheese melt evenly. Add salt and pepper. If the soup is too thick, add a little more broth or water to thin it out to your liking.
Serve soup immediately with a sprinkle of bacon on top and a fresh pretzel roll.