In a Dutch oven or large pot, melt the butter over medium heat. Add the onion and cook until soft and translucent, 3 to 4 minutes. Add the garlic and red pepper flakes and cook until fragrant, about 1 minute. Sprinkle the flour over the top and cook, stirring, until golden brown, 1 to 2 minutes
Slowly whisk in the beer, then add the chicken broth, milk, and heavy cream. Bring to a simmer and cook until thickened, 8 to 10 minutes. Whisk in the salt, black pepper, dijon mustard, and Worcestershire sauce.
Reduce the heat to low and gradually add the cheddar and fontina, a handful at a time, whisking well between additions, until melted and combined, 3 to 5 minutes.
Top the soup with a sprinkling of chives and serve.