Preheat the oven to 180C/350F/Gas 4. Grease and line six dariole moulds. Roughly chop one-third of the apricots. Halve the remaining apricots.
Heat the sugar in a saucepan until it begins to caramelise, add the apricot halves and cook for 4-5 minutes, or until softened. Set aside to cool.
For the base, cream the sugar, butter and lemon zest in a bowl until fluffy. Gradually whisk in the eggs, then fold in the flour. Fold in the uncooked chopped apricots.
Spoon the caramelised apricot halves into the bottom of the dariole moulds, then top with the cake mixture, cover with aluminium foil and transfer to a large baking tray. Fill the baking tray with enough water to come halfway up the moulds (this is called a bain-marie). Bake in the oven for 40-50 minutes, or until risen and golden-brown.
To serve, mix the apricot brandy and custard together until well combined. Turn one pudding out onto each of six serving plates and serve the custard alongside.