In a bowl toss the sliced apples with the melted butter and the vanilla. Mix well.
Sprinkle with the flour, brown sugar, cinnamon and cardamom. Mix well again.
Spread the apples in an even layer on a parchment lined baking sheet.
Gently lay the pastry over the apples. Use a fork to press all around the edges of the pastry to seal the edges and use a knife to poke a few vents in the pastry.
Bake at 375 for 30-40 minutes until pastry is cooked and golden.
Lay another sheet of parchment on top of the tart and gently lay another baking sheet on top. Flip the pans over and remove the top parchment. Let the tart cool slightly before cutting and serving.