Peel, core and quarter apples. Coat bottom and sides of a 10-inch (25 cm) cast iron or other heavy-bottomed skillet with butter; sprinkle evenly with sugar and cinnamon. Beginning at outside edge of pan, make a concentric circle by placing apple slices tightly together, flat side down. (The apple edges will rise above the top of the pan.)
Place pan on a burner set to medium-high heat. The sugar will begin to caramelize and mix with the juices. Do not disturb apples as the sauce boils. Cook for 20 minutes until the caramel is golden brown.
Transfer pan to centre of a 375ºF (190ºC) oven; cook for 30 minutes, or until apples are soft. Place foil or baking sheet on lower rack to catch any spillovers.
Roll puff pastry out to a 12-inch (30 cm) round. Remove pan from oven and place pastry on top, using a knife to tuck pastry edges around apples. Bake for another 30 minutes, until pastry is golden brown and crisp. Set aside to cool. Using a mixer, beat together amaretto, icing sugar and whipping cream until stiff and fluffy.
When tart has cooled to room temperature, tip it out onto a tray. Slice as you would an apple pie. Sprinkle with toasted almonds and garnish with a generous dollop of whipped cream.
Makes 8 servings.