Step 1: Begin by grating your sharp cheddar cheese and setting it aside. Toast your bread slices to a light golden brown. You want them sturdy enough to hold the rarebit mixture but still soft enough to absorb some of the flavor.
Step 2: In a medium saucepan over medium heat, melt the butter. Once melted, whisk in the flour and cook for about 1-2 minutes, stirring constantly, until a thick paste (roux) forms.
Step 3: Gradually whisk in the ale (or milk/non-alcoholic beer), a little at a time, making sure to incorporate it fully after each addition to prevent lumps. Continue whisking until the mixture is smooth and begins to thicken slightly, about 3-5 minutes.
Step 4: Reduce the heat to low. Add the grated cheddar cheese to the saucepan, stirring constantly until the cheese is completely melted and the sauce is smooth and creamy. Be patient and keep the heat low to prevent the cheese from seizing or becoming stringy.
Step 5: Stir in the Dijon mustard, Worcestershire sauce, cayenne pepper (if using), salt, and black pepper. Taste and adjust seasonings as needed. The sauce should be rich, savory, and slightly tangy.
Step 6: Preheat your broiler (or grill). Place the lightly toasted bread on a baking sheet. Spoon a generous amount of the rarebit mixture evenly over each slice of toast, spreading it almost to the edges.
Step 7: Broil for 2-4 minutes, keeping a close eye on it, until the top is bubbly, golden brown, and slightly caramelized. Serve immediately.