Photograph: Karen Thomas
Preheat the oven to 180°C, fan 160°C, gas 4. Peel, core and chop three of the apples. Heat half the butter with half the sugar and half the cinnamon in a frying pan until bubbling; add the chopped apples. Turn up the heat and cook the apples until they start to soften and begin to caramelise. Set aside to cool.
Grease and line a 2lb loaf tin (approximately 11 x 21cm base measurement) with baking paper, so that it comes a few centimetres higher than the edge of the tin all the way round.
Whiz the ginger snaps in a food processor to make fine crumbs and transfer to a bowl. Add the melted butter and mix well. Press the mixture into the base of the prepared tin; bake for 5 minutes. Spoon the cooked apples (and their juices) over the biscuit base in the tin.
Using an electric whisk, beat the cream cheese, ricotta, flour, sugar, vanilla, eggs and yolk together in a large bowl. Pour into the tin over the apples and biscuit base. Bake the cheesecake for 1 hour until set but slightly wobbly in the centre. Leave to cool, then chill overnight.
Core and slice the remaining apples. Heat the rest of the butter, sugar and cinnamon in the frying pan and cook the apple slices until soft and caramelised; set aside to cool. Serve the cheesecake topped with the apple slices and decorate using the cinnamon sticks.
Get ahead: bake the cheesecake up to 2 days ahead; chill. Prepare the apples for the topping a few hours ahead.
Kitchen secret: lining the tin with baking paper makes it easy to lift out the cheesecake once it has cooled.