Step 1

In a large saucepan, cook the bacon over moderate heat until the fat is rendered and the bacon is crisp, 7 minutes. Using a slotted spoon, transfer the bacon to a bowl. Add the celery, onion, jalapeño, garlic and thyme to the saucepan and cook over moderate heat, stirring, until softened, 8 minutes. Add half of the beer and cook until reduced by half, 5 minutes. Add 2 1/4 cups of chicken broth and bring to a simmer.

Step 2

In a small skillet, melt the butter. Add the flour and cook over moderate heat, stirring, until lightly browned, about 2 minutes. Whisk this roux into the soup until incorporated and bring to a simmer. Cook until thickened, about 8 minutes. Add the heavy cream, cheddar cheeses and the remaining beer and simmer, stirring occasionally, until thick and creamy, about 5 minutes. Stir in the bacon and season with salt and pepper. Add a few tablespoons of broth if the soup is too thick. Serve the soup with garlic toasts.