Photograph: Jan Baldwin
To make the ice cream, slowly heat the sugar in a heavy-based pan, swirling the pan, until it dissolves. Bubble until it caramelises and turns a dark caramel colour. Add the milk and cream (it will bubble and spit), stir until smooth and bring to the boil.
Whisk the egg yolks in a bowl. Pour in the caramel mixture, stirring all the time. Return the mixture to the pan and cook over a gentle heat until it's thick enough to coat the back of a spoon. Carefully strain into a bowl and leave to cool. Churn the mixture in an ice-cream maker, then freeze until ready to use. Alternatively, pour into a freezer box, cover and freeze, folding the ice crystals from around the edge into the centre every couple of hours.
To make the tart, preheat the oven to 200°C, fan 180°C gas 6. In a bowl, cream together the butter and sugar. Mix in the egg white, followed by the flour and ground almonds. Roll out the pastry on a lightly floured surface to a circle about 23cm in diameter (use a large dinner plate as a guide). Place it on a baking sheet and spread the almond mixture over the pastry, leaving 2.5cm around the edge free. Fan the apple slices in circles on the almond mixture, overlapping each other, then fold the pastry edge over and crimp the edges. Dust with icing sugar and bake for 30 minutes.
Remove from the oven and place a sheet of nonstick baking paper over the tart and then another baking tray on top. Carefully flip the trays over so the tart is now upside-down and remove the top baking tray. Place back in the oven for another 15 minutes until the pastry is cooked through. Remove from the oven; flip the tart back over on to a serving plate and serve warm, dusted with icing sugar and with a scoop of the caramel ice cream.
Get ahead: make the ice cream a couple of weeks ahead. Make the tart a few hours ahead and serve at room temperature.