To make the pastry, put the flour, sugar and butter in a bowl. Work it all together with your fingers until you have a sandy mixture. Add the egg, extra egg yolk and vanilla and carry on mixing until you have a smooth ball. Wrap it up in plastic wrap, flatten and put it in the fridge for about 30 minutes.
Meanwhile, peel and core the apples and cut them into chunks. Put half the butter in a non-stick pan and add the apple chunks, the brown sugar and a tablespoon of water. Put the lid on and cook over medium heat for about 15–20 minutes until the apples collapse and turn slightly golden on the bottom. Stir in the cinnamon and squash the apples into a purée with a wooden spoon. Remove from the heat.
Preheat the oven to 200°C (400°F/Gas 6). Roll out the pastry on a sheet of baking paper to a circle of roughly 32–34 cm(12–13 inches), dusting with a little plain flour if necessary. Using the baking paper, flip the pastry over into an ungreased 24 cm(9½ inch) springform tin. Let it settle in before peeling off the paper and pressing the pastry onto the base and side of the tin. Don’t worry if the pastry tears, just patch it and press the gaps together.
Spread the apple purée over the base and put the apricots on top. Scatter with caster sugar, more or less, depending on the sweetness of your fruit. Dot with the rest of the butter, then fold the pastry edge in and over to cover the edge of the filling. Bake for about 40 minutes, or until the top of the fruit is golden brown in places and the pastry crisp. Serve plain or with yoghurt and whipped cream.