Place a medium saucepan over medium heat and melt the butter.
Sprinkle the flour into the melted butter and whisk constantly for 1 to 2 minutes to cook out the raw flour taste, creating a smooth roux.
Slowly pour in the beer while whisking vigorously to prevent lumps. Continue cooking until the mixture bubbles and thickens slightly.
Reduce the heat to low. Gradually add the shredded sharp cheddar cheese one handful at a time, whisking constantly until each batch is fully melted and the sauce is smooth.
Stir in the garlic powder, onion powder, paprika, salt, and black pepper.
Simmer on low for an additional 2 to 3 minutes to ensure flavors meld and the dip is heated through. Do not let it boil vigorously or the cheese may separate.
Transfer to a serving bowl immediately and serve warm with soft pretzels, crackers, or bread cubes.