Place a large skillet over medium-high heat. Add ground chorizo and cook until it is fully browned and cooked through. Drain grease and set to the side.
Melt the butter in a saucepan over medium heat. Create a roux by adding the flour to the melted butter. Stir continuously as flour cooks for 2-3 minutes.
Slowly add milk and then beer to the roux, whisking until it is fully combined.
Turn the heat up to medium-high and bring the mixture to a simmer.
Add ground mustard, Worcestershire sauce, and hot sauce (if using). Continue cooking for 5-6 minutes or until the mixture thickens.
Add cheddar cheese and smoked Gouda cheese a little at a time. Stir in the cheese until all of it has been added and the mixture is smooth.
Add cooked chorizo and stir to combine. Add salt and pepper to taste. Serve warm.