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For the pastry, rub the butter into the flour, sugar and a pinch of salt in a bowl until crumbly. Mix in the egg until it forms a dough, then form into a puck shape. Cover and chill for at least 30 mins. Will keep chilled for two days.
Heat the oven to 200C/180C fan/ gas 6. Roll the pastry out on a lightly floured surface to roughly the thickness of a £1 coin, and use to line a 23cm fluted tart tin, leaving some overhanging. Line with a disc of baking parchment big enough to cover the edges, and fill with some baking beans to weigh it down (use dried rice or lentils if you don’t have baking beans). Bake for 15 mins, then remove the parchment and beans and bake for 10-15 mins more until the pastry is biscuity. Trim away any overhanging pastry with a serrated knife. Set aside to cool.
Meanwhile, set aside four of the apples, then peel, core and roughly chop the rest. Put them in a shallow saucepan with 2 tbsp water, all but 1 tbsp of the sugar and the alcohol, if using. Cover and cook over a low heat for 25-30 mins, stirring occasionally and adding more water if needed, until the apples have collapsed into a purée. Taste the mixture and sweeten with more sugar, if needed.
Turn the oven up to 210C/190C fan/gas 8. Peel, core and halve the reserved apples, then cut into even-sized slices. Spread the apple purée over the base of the tart case, then arrange the apple slices in neat, concentric circles, starting from the outside. Brush the apples with butter, then scatter over the reserved sugar and bake for another 20-25 mins until golden.
Mix the jam with 1 tbsp hot water from a freshly boiled kettle. When the tart has finished baking, glaze generously with the jam, then leave to cool a little. Serve warm or cold, dusted with icing sugar, if you like.