How to Make It
In a large bowl, toss the apple quarters with the cinnamon, ginger, salt, nutmeg, allspice and cloves.
In a 12-inch nonstick skillet, melt the butter over moderate heat. Add the sugar and cook, swirling the mixture, until a deep caramel forms, about 7 minutes. Remove from the heat.
Preheat the oven to 400°. Arrange the apple quarters side by side in a ring around the skillet with the points facing in. Fill the center with as many apple quarters as possible. Lay any remaining apples on top (the apples can be packed down as they shrink). Cover and cook over moderate heat until the apples are tender, 15 to 18 minutes.
Meanwhile, on a lightly floured work surface, roll out the puff pastry about 1/8 inch thick. Cut out a 14-inch round and transfer it to a baking sheet. Refrigerate until chilled, about 10 minutes.
Drape the pastry round over the apples and tuck in any overhang with a rubber spatula. Make two 2-inch slits in the center of the pastry. Bake for about 30 minutes, until the pastry is golden brown and cooked through. Remove from the oven and let stand for 10 minutes. Cover the tart with a large plate and very carefully invert the tart onto the plate. Serve the tart in wedges with a dollop of crème fraîche or whipped cream.