Dice the bacon, chop the vegetables and mince the garlic before you turn on the heat. Shred both cheeses and set them aside. Once the pot is hot, the steps move fast, so having everything ready helps.
Add the bacon to your cold Dutch oven and turn the heat to medium. Cook until the pieces turn golden and crisp, stirring now and then. Lift the bacon out with a slotted spoon and save it for topping.
Leave a few spoonfuls of bacon fat in the pot and drain the rest. Add the celery, onion and jalapeño and cook until they turn soft. Stir in the garlic and thyme for one minute until the kitchen smells amazing.
Drop the butter into the pot and let it melt over the vegetables. Sprinkle in the flour and stir constantly for about two minutes. This cooks off the raw flour taste and forms a thick paste.
Pour in the beer slowly while stirring so no lumps form. Let it bubble for a few minutes, then whisk in the chicken broth. Simmer gently for about 15 minutes until the soup thickens slightly.
Lower the heat and pour in the heavy cream. Stir well and warm it through, but don't let it boil hard. A gentle heat keeps the cream smooth and prevents splitting.
Add the cheese one handful at a time, stirring after each addition. Wait until each batch melts before adding the next. This slow method gives you a velvety soup with no clumps.
Taste the soup and add salt and pepper if it needs them. Fold in most of the bacon and keep a little for the top. Ladle the soup into warm bowls and serve with garlic-rubbed toasts.