Make the Roux: Melt the unsalted butter in a medium heavy-bottomed saucepan over medium heat. Whisk in the all-purpose flour and cook for 1 to 2 minutes, whisking constantly until bubbly and pale golden (this eliminates any raw flour taste).

Whisk in Beer & Milk: Slowly pour in the amber ale in a steady stream while whisking vigorously to prevent lumps. Whisk in the whole milk. Bring to a gentle simmer and let cook for 2 to 3 minutes until slightly thickened and smooth.

Melt Cream Cheese & Seasonings: Reduce heat to low. Whisk in the softened cubed cream cheese, Dijon mustard, Worcestershire sauce, garlic powder, smoked paprika, cayenne pepper, and kosher salt. Whisk until the cream cheese is completely melted and incorporated into a silky sauce.

Gently Melt the Cheeses: Remove the saucepan from the direct heat (or keep on the lowest heat setting). Add the freshly grated sharp cheddar and Gruyere cheese one handful at a time, whisking gently in one direction until completely melted before adding the next handful. (Pro tip: Gentle off-heat melting prevents the cheese from separating or becoming grainy!).

Garnish & Serve Warm: Taste and adjust salt or cayenne to your liking. Pour the warm beer cheese dip into a preheated mini cast-iron skillet or warm ceramic bowl. Garnish with sliced fresh chives and a dusting of smoked paprika. Serve immediately with warm salted soft pretzel bites, tortilla chips, and crisp vegetable sticks!