In a medium saucepan over medium heat, melt butter. Add minced garlic and cook for about a minute until fragrant, don't let it brown.

Add all-purpose flour to the butter and garlic. Whisk constantly for about 1 minute to cook out the raw flour taste. The mixture will look like a thick paste.

Slowly pour in room-temperature beer while whisking constantly. Keep whisking until smooth and combined. Then pour in whole milk and whisk again until fully incorporated.

Whisk in Dijon mustard, Worcestershire sauce, smoked paprika, and cayenne pepper. Bring the mixture to a gentle simmer over medium heat, whisking frequently, until it thickens slightly, about 3 to 4 minutes.

Reduce the heat to the lowest setting. Add sharp cheddar and gruyère one small handful at a time, whisking after each addition until fully melted before adding the next. Season with salt and black pepper, taste and adjust.

Transfer to a warm serving bowl or keep in the saucepan on the lowest heat. Serve immediately with soft pretzel bites, toasted bread, or veggies. If it thickens as it sits, whisk in a small splash of warm beer or milk to loosen it back up.