1) For the mousse, place the apples and lemon juice and a little bit of water in a pan, bring to a boil. Reduce the heat and cover with a lid, cook for about 7-9 min until the apples are tender. Stir in the sugar until dissolved. Cool down.
2) Puree the mixture in food processor with the Calvados. Melt the gelatine and add it once the puree is done, fold in the whipped cream, then place into an individual mould or ramekin. Place in the freezer for an hour.
3) For the tart tatin, peel the apple, cut it in half, remove the core from both halves. In a small pan place the room temp butter, sugar and spices.
4) Cover the apple with the puff pastry making sure it is well stuck. Place it on top of the pan and cook until you get a caramel colour. Finish to cook in the oven at 180 degrees for about 6-8 min, the puff pastry should look golden brown and should feel crisp.
5) For the granite, make a syrup with the sugar and water. Chop the apple removing the core (keep the skin for extra flavour). Place into a food processor with the lemon juice until all the juice comes out of the apple.
6) Place it in a square container in the freezer, leave for one hour before you can start breaking the texture with a fork. You will have to do this every hour until the granite is formed.