In a large pot on medium heat, melt the butter, when melted, add the onion, thyme, white and cayenne pepper, and cook until onion is tender, stirring often, about 3-5 minutes.
In a mixing bowl, whisk together the broth, beer, and 2 tablespoons of cornstarch. Whisk until the cornstarch is mixed in fully.
Stir broth mixture into the pot. Bring the pot to a boil then reduce heat.
Simmer 5 minutes, then stir in the cream.
In a mixing bowl, toss the shredded cheese with the remaining tablespoon of cornstarch.
After the cream is mixed in, gradually add the shredded cheese to the soup, stirring until the cheese is mixed in before adding more cheese. Repeat until the cheese is all mixed in. Taste and add hot pepper sauce as desired.
Ladle into bowls and enjoy.