Blind bake crust. Fit the pie dough to a 10 inch tart pan, pressing it firmly onto the sides and bottom. Wrap the crust in plastic wrap and place in the freezer for at least 30 minutes - over night is fine too. Preheat the oven to 400°F (200°C). Place the unwrapped, frozen tart shell in the oven to bake for 12 minutes. Remove from the oven and allow to cool.
Prepare apples. Meanwhile, peel the apples and then cut them into quarters and slice out the core. Slice each quarter into four slices.
Prepare custard. Beat the eggs until they are frothy. Beat in the sugar until the mixture thickens slightly (about 1 minute with a hand mixer). Beat in the ground almonds, heavy cream and brandy.
Assemble. Place the apple slices in an attractive pattern in the tart shell (this is totally optional - you can just toss them in there as well). Pour the egg mixture on top of the apples and sprinkle the sliced almonds on top.
Bake. Carefully place the tart in the oven and lower the oven temperature to 375°F (190°C). Bake for 35 minutes.
Serve. Serve the Tarte Normande while it is still warm, perhaps with a dollop of sweetened whipped cream or crème fraîche. You can even spike the cream with a little Calvados if you wish.