Position an oven rack about 5 inches below the broiler and heat the broiler on high. Place the bread on a baking sheet and broil for 1 to 2 minutes per side, watching closely, until lightly toasted. Remove the sheet from the oven.
Melt the butter in a small saucepan over medium heat. Whisk in the flour and cook for about 1 minute, stirring constantly, until the mixture looks smooth and lightly foamy.
Gradually whisk in the ale or milk. Cook for 1 to 2 minutes, whisking, until the sauce thickens slightly. Reduce the heat to low.
Add the shredded cheddar a handful at a time, whisking until each addition melts before adding the next. Do not let the sauce boil after the cheese is added. Stir in the Dijon mustard, vegetarian Worcestershire-style sauce, paprika, cayenne, and black pepper.
Divide the cheese sauce among the toasted bread slices, spreading it all the way to the edges. Broil for 2 to 4 minutes, until the topping is bubbling and browned in spots. Watch continuously because broilers vary.
Let the rarebit stand for 1 minute, then serve hot with fruit, sliced tomatoes, or a simple green salad.