I've always understood it to be glorified cheese on toast. Here's what Gary Rhodes has to say in his <i><b>New British Classics</b>
The origin of the name 'rarebit' or 'rabbit' has been disputed for centuries. Some say the former comes from the dish's position in the meal, as a 'rear-bit' (rather as an hors d'oevre was known at one time as a 'fore-bit'); the latter is either a corruption of this, or reflects the patience of the Welsh huntsman's wife when he came home empty-handed from the chase, and she had to prepare cheese instead ...
There are also many different recipes. Toasted cheese recipes appear in cookery books throughout the centuries, and there are English Rabbits, Welsh Rarebits, Buck Rarebits and Scotch Rabbits, all of them subtly different. This is my version, and this recipe is really the minimum amount you can make for a successful mixture. It will keep in the fridge for up to ten days and also freezes well, so can be used in plenty of other dishes. <b>It's also delicious as a simple cheese on toast.</b> When I make it at home, I divide it into two and freeze the other half for use later.
WELSH RAREBIT MIX
350g mature Cheddar cheese, grated
85ml milk
25g plain flour
25g fresh white breadcrumbs
1/2 tbsp English mustard powder
A few shakes Worcestershire sauce
1 egg
1 egg yolk
Salt and pepper.
Put the Cheddar into a pan and add the milk. Slowly melt them together over a low heat, but do not allow the mix to boil as this will separate the cheese. When the mixture is smooth and just begins to bubble, add the flour, breadcurmbs and mustard and cook for a few minutes, stirring, over a low heat until the mixture comes away from the sides of the pan and begins to form a ball shape. Add the Worcestershire sauce, salt and pepper and leave to cool.
When cold, place the mixture into a food processor, turn on the motor and slowly add the egg and egg yolk. (If you don't have a processor or mixer, just beat vigorously with a wooden spoon.) When the eggs are mixed in, chill for a few hours before using. After it has rested in the fridge, you will find the rarebit is very easy to handle and has so many uses.</i>
<b>So, whilst I would have agreed with your boss before reading this, I think there is a valid argument on both sides. The Welsh Rarebit, it seems, is the topping mixture (which includes both bread and eggs as well as cheese) and serving it on toast is just one of many options. Gary Rhodes includes a recipe (his favourite) for Smoked Haddock with Welsh Rarebit, with not a piece of toast to be seen!</b>