Place the hazelnuts on a cookie sheet and roast in the hot oven for 7 to 8 minutes. Transfer the nuts to a food processor, add the ¼ cup sugar, egg, butter, and vanilla extract. Process until creamy paste forms.
Roll out the puff pastry to 15 inches long by 10 inches wide. Transfer it to a parchment-lined cookie sheet. Spread the frangipane on the dough stopping about 1 ½ inch away from the edges.
Arrange the apple slices over the frangipane on an overlapping pattern to cover well the frangipane underneath. Fold the edge of the dough over the apples to make a 1 to 1 ½ inch border.
Sprinkle 2 to 3 tablespoons sugar over the apples letting some of the sugar sprinkled over the border dough. Break the 2 tablespoons of sweet butter and scatter them over the apples. Bake for 1 hour the dough should be nicely crystallized all over.
Remove the finished tart from the oven and cool on a wire rack until still a bit warm to the touch. Mix together the orange marmalade with the Calvados and glaze the surface of the tart spreading it carefully on the apples and the border crust. Use the back of the spoon to easily spread.
Serve at room temperature cut into small wedges. Serve with whipping cream or ice cream.