A "magic cake" has three layers, each with its own texture and flavour (a dense and moist base, a middle cream layer, and a light sponge top). It's called magic because the cake divides into these layers during the baking.
The ingredients aren't unusual: You just need eggs, sugar, flour, butter, and milk. The three-in-one cake happens through slow baking, as The Telegraph explains:
The egg yolks, beaten with the sugar, butter, flour and milk, form the first two layers of the magic cake: the base and the cream. What happens is that slow cooking at 150C/300F/gas mark 2 allows the bottom of the cake to cook like a cake without cooking the upper part, which retains its creamy texture.
The tricks to making this magic cake is to incorporate the egg whites gently into the liquid mixture (you don't want it to dissolve into the batter, and large lumps are good) and to beat the egg yolks and sugar together well.
The photo above is a classic vanilla magic cake, but you can make other variations or three-layer brownies. Certainly an interesting way to switch up your cakes and brownies.
Magic cakes: the miraculous recipes that make three cakes in one [The Telegraph]