This dessert is formed as a galette, which is just a fancy French cooking term for “round.” In this case, you don’t put the pastry dough in a pie or tart tin. Just roll it out, fill the center with fruit and then fold over the pastry edges on to the fruit and brush the pastry with a little egg wash.
In a large bowl rub the butter and lard/shortening into the flour, sugar and salt until mixture resembles coarse meal. Add the water and vinegar and mix until moist clumps form, adding more water by teaspoonfuls if dough is dry. Gather dough into ball; flatten into disk. Wrap in plastic and refrigerate at least 30 minutes.2.
Melt the butter in a large skillet. Add the apples and sauté until they start to soften — about 10 minutes. Add the cardamom and cinnamon and 1/3 cup of the honey, stir in and cook 1 minute. Take it off the stove and allow to cool to lukewarm.3.
Preheat an oven to 350°F. Roll out dough to about a 12-inch round and place on a baking sheet. Spoon half of apple mixture over crust, leaving 2-inch plain border. Sprinkle dates and nuts over the apples. Top with remaining apple mixture. Fold outer edge of crust over apples (dough is delicate; press together any tears). Whisk egg and milk in bowl. Brush edges generously with egg mixture. Sprinkle the crust with the demerara sugar.4.
Bake until crust is golden brown, about 35 minutes. Cool for about 45 minutes. Whip the cream with the sugar, cinnamon and vanilla until stiff and serve with the pastry.