Make the pastry: put the flour into a large bowl. Rub in the butter and vegetable fat until the mixture resembles fine breadcrumbs. Mix in enough water to make a soft, pliable dough. Roll out the pastry on a lightly floured work surface and use to line a 19cm loose-bottomed fluted flan tin. Reserve the trimmings for decorating the tart and chill the tart in the refrigerator for 30 minutes.
Melt the butter in a saucepan, stir in the caster sugar, and cook for about 1 minute. Remove from the heat, leave to cool a little, then gradually stir in the egg, cornflour or semolina, and almond extract.
Spread the jam evenly over the bottom of the pastry case, and pour the almond mixture on top.
Roll out the reserved pastry trimmings, and cut into strips that will fit across the tart. Arrange the strips on top of the almond filling to form a lattice, attaching them to the pastry case with a little milk.
Bake on a hot baking tray in a preheated oven at 200°C/gas mark 6 for 45–50 minutes until the filling is well risen and golden and springs back when lightly pressed with a finger. If the pastry is browning too much, cover the tart loosely with foil.
Remove the tart from the oven. Sprinkle with icing sugar and serve the tart warm or cold.