Bring the cheeses to room temperature. Cube the cheeses into roughly evenly sized pieces.
In a soup pan, melt half of the butter over medium heat. Add the peas, carrots, garlic, celery, and chopped shallot, and sauté until just beginning to brown.
Add the remaining butter to the pan, followed by the flour - 1 tablespoon at a time. Stir until the vegetables are covered.
Pour the chicken broth into the pan. Stir until the flour is dissolved and a thick soup base has formed. Simmer for 5 minutes.
Reduce the heat to medium-low and add the heavy whipping cream. Then add the cheese, a few cubes at a time, to the base. Continue to stir until the cheese has completely melted into the soup.
Slowly pour in the beer, stirring to incorporate. Take care not to pour too fast and create foam that might overflow. Reduce the heat to low and let the soup simmer for an additional 5 minutes.
The soup will begin to thicken as it cools. Serve right away with croutons and freshly grated white cheddar cheese. Enjoy and stay warm!