For the pastry, place the flour, sugar, salt and butter in a large mixing bowl and, using a pastry blender or a butter knife, cut the butter into the flour until you are left with small pea-sized lumps of butter.
In a measuring jug, whisk together the egg, vinegar and ice water until combined. Make a well in the centre of the flour and butter mixture and pour in the liquid.
Using two large forks, gently toss all the ingredients together until the dough takes shape and begins to hold together. Turn the dough out onto a layer of cling film and wrap. Place in the fridge to chill for a good 30 minutes before rolling out.
Preheat the oven to 200˚C.
Place the cooking apples in a bowl with the remaining ingredients for the filling and set aside
Roll out the pastry to a disc, about 5mm in thickness, on a floured work surface. Transfer to a flat baking tray lined with parchment paper.
Place the apples in the centre of the pastry disc, leaving at least 4cm around the sides. Fold the edges of the pastry inward, over and around the apples, leaving the center exposed. Brush the outside edges of the pastry with beaten egg. Bake in a hot oven for 40 minutes until golden brown and the apples are tender when pierced with a fork.
While the galette cooks, in a bowl whisk the cream with the sugar, cardamom and vanilla bean paste until thickened.
Remove the cooked galette from the oven and let it cool until just warm. Serve with dollops of the freshly whipped cream.