Freshly grate the sharp cheddar cheese. Set aside.
In a large saucepan over medium heat, add the butter and flour. Whisk until the flour has been absorbed by the melted butter, and forms a paste.
Gradually pour in the whole milk as you whisk.
Slowly pour in the beer and whisk another minute, until thickened up slightly.
Whisk in the Worcestershire sauce, dijon, garlic powder, and smoked paprika.
Add in half of the grated cheese and stir until completely melted. Stir in the remaining until a smooth yet thick cheese dip. Season with salt and black pepper to taste. Enjoy with the homemade pretzel bites and cooked sausage!