Melt Butter: In a medium saucepan, melt the butter over medium heat.
Make Roux: Add the flour and whisk continuously for about 1-2 minutes until it forms a smooth paste and starts to bubble slightly, but do not let it brown.
Add Liquids: Gradually add the beer, whisking constantly to combine. Then add the milk slowly, continuing to whisk to ensure a smooth mixture.
Season: Stir in the Dijon mustard, garlic powder, onion powder, and smoked paprika. Continue to cook for a few minutes until the mixture thickens.
Add Cheese: Reduce the heat to low and slowly add the shredded cheddar cheese, one handful at a time, whisking until melted and smooth.
Season to Taste: Taste and season with salt and pepper as needed.
Serve: Pour into a serving bowl and enjoy with your favorite dippers such as pretzels, bread, or vegetables.