4 tablespoons unsalted butter
1/2 yellow onion, finely chopped
1 stalk celery, finely chopped
2 small carrots, finely chopped
1 clove garlic, minced
1/2 cup all-purpose flour
2 cups chicken broth
2 cups whole milk
12 ounces beer (not dark)
3 cups grated sharp Cheddar, plus more for garnishing
1 1/2 teaspoons kosher salt
1/4 teaspoon black pepper
1 tablespoon sugar
1 teaspoon hot sauce (optional)
2 tablespoons olive oil
Heat oven to 350° F.
Melt the butter in a large saucepan over medium heat. Add the onion, celery, carrots, and garlic. Cook until softened, 5 to 7 minutes. Stirring constantly, add the flour and cook for 3 minutes; the mixture will clump. Still stirring constantly, add the broth slowly and cook until a thick, smooth paste forms, 3 minutes. Still stirring, slowly add the milk, then the beer. Cook until the foam subsides and the mixture thickens slightly, about 5 minutes. Add the Cheddar, salt, pepper, sugar, and hot sauce (if using) and simmer over medium-low heat for 20 minutes, stirring occasionally. Let cool for 5 minutes.
Meanwhile, thinly slice the baguette. Arrange on a baking sheet and brush with the oil. Bake until golden, 13 to 15 minutes. Ladle the soup into individual bowls and top with additional grated Cheddar and the baguette slices.
Tip: Use a beer that's light in flavor, like a lager or a pale ale. The darker the beer, the more bitter the soup will taste.