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What a strange name for a simple and tasty dish. There are no discernible bubbles in it and it doesn't squeak... mostly (see below).
Bubble and squeak is a triumph of thriftiness in that it uses leftover vegetables1. Many a British Monday lunch or dinner has consisted of the remains of the Sunday roast served with bubble and squeak.
How to Make It
The primary ingredient is mashed potatoes, comprising between 50% and 75% of the dish, accompanied by a green vegetable, usually cabbage.
Mix these together in a bowl and add salt and pepper to taste2. Place a frying pan on a medium to high flame or medium-hot electric ring and when heated, add a knob of lard3. As soon as the fat has melted, spoon in the potato/cabbage mixture and flatten it to cover the bottom of the pan in a round cake about 1" (2.5cm) thick. This is when you might hear it 'squeak'. When the bottom has a golden brown crust on it, flip the bubble and squeak over and cook the other side.
As a side dish serve it with cold meat and your choice of pickle. For breakfast have your eggs, bacon, sausages, baked beans, fried tomatoes, fried mushrooms, black pudding, and fried slice with a dollop of bubble and squeak. Any self-respecting British caff should have bubble on the menu.
Of course, there are almost as many ways of making bubble and squeak as there are people who make it. Any of the following ingredients can be mixed in with the potatoes - cabbage, cauliflower, peas, broccoli, carrots, onion, mushrooms, or perhaps a little grated cheese. You might even experiment with some flavourings - garlic, herbs, nutmeg, or if you're feeling adventurous, Tabasco. Don't overdo it though - bubble and squeak is best when kept simple.
In some parts of the UK it's not uncommon to include the leftover meat and have the bubble and squeak as a meal in itself, rather than serving the bubble and squeak as an accompaniment to the meat.
How Did It Get that Name?
It's likely that it's because the ingredients are first boiled - giving us the bubbles, and then fried producing the squeaking noises already mentioned.
The term 'bubble and squeak' is mostly used in southern Britain. In the north of England and in Wales it's known as 'fry-up', and may be called 'stovies' in Scotland.