In a medium saucepan, on medium-low heat, melt the butter; add the flour and whisk until smooth.
Add the miso paste, if using; mix until fully incorporated.
Cook, whisking, until mixture is bubbling and smells nutty; about 3 minutes.
Gradually add beer and milk; whisk together until smooth.
Cook on medium-low for 4 to 5 minutes; stirring occasionally, until thickened.
Remove from the heat; add the cheese and whisk until melted and well incorporated; the beer cheese dip will continue to thicken as it cools.
Stir in the garlic powder, onion powder and smoked paprika, if using.
Taste and add salt, if necessary.
Serve with pretzels, vegetables or crusty bread.