Place apples and cider in a large bowl and stir well.
Cover with plastic wrap and allow to macerate for 1 hour.
Drain.
On a flat, lightly floured work surface, roll out puff pastry dough to form a 30 cm (12-inch) long by 23 cm (9-inch) wide rectangle measuring 3 mm (1/8 inch) thick.
Cut pastry into thirds lengthwise and into quarters across the width.
You should have twelve 7.5 cm (3 inch) x 7.5 cm (3 inch) squares.
Prick dough with a fork and brush with the diluted egg yolk.
Transfer pastry squares to a baking sheet and bake for about 8 to 10 minutes, or until golden.
Reserve.
In a small saucepan, stir together 125 mL (1/2 cup) brown sugar, evaporated milk and corn syrup.
Cook over medium heat, stirring often, until syrup is hot.
Cover and reserve.
Melt butter in a skillet over medium-high heat.
Add apples, remaining brown sugar, ginger, cinnamon and cardamom.
Cook for about 10 minutes, or until apples are golden and caramelized.
Spoon 5 mL (1 tsp.) caramel sauce into the centre of each of four dessert plates.
On each plate, place one puff pastry square on the caramel and top with apple mixture.
Cover with a second pastry square and more apples; top with the third and final pastry square.
Drizzle caramel sauce over each mille-feuille and serve with vanilla frozen yogurt.