In a large bowl, gently combine apples with sugar, lemon zest, lemon juice, vanilla, cardamom, and flour.
Roll out the dough. Starting in the center, arrange the apples in overlapping rows or circles, leaving a 2-inch border. Brush melted butter over the top of arranged apples.
Pleat the dough, brush with egg mixture, and sprinkle with sugar. Bake for 30 minutes and then cover with tented foil and bake for 30 minutes longer.
Serve with vanilla ice cream and salted caramel sauce.