Fry the bacon in a large stockpot or Dutch oven over medium-high heat until crisp, 5 to 10 minutes. With a slotted spoon, transfer the bacon to a paper towel-lined plate and set aside.
Add the onion and shallot to the pot containing the bacon drippings and cook, stirring occasionally, until softened, about 4 minutes. Add the potato, carrot, celery, and garlic and cook until the garlic is fragrant, about 1 minute. Add the flour and cook, stirring to coat the vegetables, until the mixture begins to brown on the bottom of the pot, about 2 minutes.
Gradually whisk in the ale, chicken stock, and half-and-half. Add the bay leaf and increase the heat to medium-high. Bring to a boil, reduce the heat to medium-low, and simmer until the vegetables soften, about 3 minutes.
Remove the pot from the heat. Stir in the cayenne and sherry and allow to cool slightly, about 2 minutes. Slowly whisk in the cheese and thyme until the cheese melts. Stir in the fried bacon, season with salt and pepper to taste, and serve immediately.