Melt the butter (4 tablespoons) in a medium saucepan over medium heat. Add the flour (1/4 cup) and whisk until the flour is completely absorbed. Continue cooking, whisking constantly, for 1 minute.
In a medium saucepan, melt butter over medium heat. Whisk in the flour until the flour is completely absorbed. Cook, whisking constantly, for one minute or until it begins to toast.
Remove from heat, slowly add beer (1 cup) and a half and half (1 1/4 cup), whisking constantly.
Stir in Worcestershire sauce (2 teaspoons), hot sauce (1/2 teaspoon), dried mustard (1/2 teaspoon), garlic powder (1/2 teaspoon), and paprika (1 teaspoon) and mix until combined.
Bring the mixture to a boil, whisking constantly, then immediately reduce heat and gently simmer, whisking frequently, until the mixture is thick enough to coat the back of a spoon, about 3 minutes.
Reduce the heat to low, gradually add the cheese, about 1/2 a cup at a time, stirring to incorporate each addition. Wait to add more cheese until each addition is fully melted. Continue until all cheese is added and stir until it is melted and the mixture is smooth.
Transfer cheese mixture to a serving dish and top, if desired with chives, crumbled bacon, and extra shredded cheese.
Notes
Roux: After the flour has been added to the melted butter, it needs to be cooked for at least 1 minute. This cooks out the “flour’ taste. If you cook it longer the roux will develop a deeper flavor. Remember to whisk constantly so the roux doesn’t burn. If it does burn, throw it out and start over!
Adding Cheese: When adding the cheese to the sauce, keep the heat on low. If you add and heat it too quickly, the cheese dip can break and be ruined.