Heat the oven to 375°F with the rack in the middle of the oven.
Melt the butter, honey, vanilla and salt together in a small pan.
Brush the mixture over one sheet of phyllo dough, then sprinkle with the chopped walnuts. Drape another layer of phyllo over the walnuts and brush it with the butter mixture and sprinkle with more walnuts. Repeat this with the rest of the sheets of phyllo dough, butter mixture and walnuts, finishing with a sheet of phyllo and butter mixture, but leave the top without nuts. Fold the phyllo so that it is the same width as the pan, then trim the corners and edges to fit over the apples. You want the layered phyllo to be slightly larger so you can tuck it in around the apples a bit.
Bake for about 20 minutes or until the phyllo crust is golden brown.
Invert the Tarte Tatin onto a serving dish. If any of the caramel is left in the pan, add a bit more booze and deglaze it. Pour this caramel over the tarte. Serve it warm or room temperature with or without ice cream. Makes a great breakfast too.
Baker's Notes To use puff pastry: Preheat oven to 425°F. Roll the puff pastry out to 2 inches beyond the width of the pan. (The pastry will rise up and shrink in width, so be sure it is large enough.) Drape the rolled pastry over the cooked apples and bake for about 20-25 minutes or until the pastry is golden brown and the juices are thick. Invert onto a serving plate as instructed above. To use pie dough: Preheat oven to 375°F. Swap out the phyllo for a sheet of rolled-out pie dough that goes an inch beyond the width of the pan.