Open beer and let stand while dicing vegetables.
In a large saucepan, sauté the bacon until crisp. Remove with a slotted spoon onto paper towels. Reserve some for garnish.
Add the onion, carrot, celery jalapeno, garlic and thyme and sauté over medium heat until soft, about 7 minutes.
Add half the beer and and cook until reduced by half, about 5 minutes.
Add 2 1/4 cups of chicken broth and bring to a simmer.
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 Cayenne, salt and pepper. Add a few tablespoons of broth if the soup is too thick.