Position an oven rack 6 inches below the broiler and heat the broiler to high. Grate the cheddar.
Lightly toast the bread under the broiler until just golden and dry, 1–2 minutes per side. Set the slices on a baking sheet.
Melt the butter in a medium saucepan over medium heat. Whisk in the flour and cook, whisking, until foamy and sandy, about 1 minute.
Gradually whisk in the ale and the mustard powder until smooth. Simmer, whisking, until thickened to a light sauce, 1–2 minutes.
Reduce the heat to low. Stir in the Worcestershire sauce, cayenne, and black pepper. Add the grated cheddar a handful at a time, stirring until fully melted and glossy after each addition, 2–3 minutes total; do not boil.
Remove from the heat and let the mixture stand for 1 minute. Whisk in the egg yolk until incorporated, then taste and season with the salt.
Spoon the cheese mixture over the toasted bread, spreading to the edges to protect the crusts from burning.
Broil until the topping is bubbling and deeply browned in spots and the bread edges are crisp, 2–4 minutes. Serve immediately.