For the apples, heat a large frying pan until medium hot, add the butter and apples and cook for 6-7 minutes, or until the apples have softened.
Add the sugar and lemon zest, stirring well, and cook for 2-3 more minutes. Transfer the apples to an ovenproof dish.
Preheat the grill to medium.
For the topping, heat a saucepan until medium-hot, add half the butter and cook until foaming. Stir in the cornflour and cook for 1-2 minutes, or until thickened and smooth.
Gradually add the milk to the pan, whisking continuously, until all of the milk is incorporated and the mixture is smooth and creamy. Cook for a further 2-3 minutes, or until thickened.
Remove the pan from the heat and whisk in the granulated sugar and beaten eggs until well combined. Spoon the mixture over the apples in the ovenproof dish.
Mix the demerara sugar and ground cinnamon together in a bowl, then sprinkle over the top of the dish and dot with the remaining butter. Grill for 5-6 minutes, or until golden-brown and bubbling.
Spoon the pudding into shallow serving bowls and serve while hot.