In a large saucepan, melt the butter over medium heat. Add the carrots and leeks, season with salt and pepper and cook, stirring, until soft, 10 minutes. Add the flour and cook, stirring often, for 2 minutes.
Slowly pour in the milk, whisking constantly. Increase the heat to medium-high, add the beer and mustard and bring the soup to a boil, whisking constantly. Reduce the heat to low and simmer, whisking, until creamy and thickened, about 10 minutes.
Remove the pan from the heat. Whisk in the cheese 1 handful at a time until combined. Season to taste with salt and pepper. Top with the croutons.