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On a table, knead the pie dough and let it rest in the fridge while you prepare the rest of ingredients.
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Peel and grate the apples to have 4 cups
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On a pan, fry the apples, sugar and lemon juice.
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When the juice evaporates,take the apples away from the heat.
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Let them cool completely.
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Take the dough out of the fridge and divide to 2/3 for the skillet bottom and 1/3 for the lattice ribbons.
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Butter and flour the baking dish ( 8 cups volume)
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Preheat the oven to 180 C / 356 F.
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Roll the dough to the size that covers the bottom and the sides of the baking dish.
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Roll the remaining third of the dough and cut the ribbons for the lattice.
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Whisk the egg whites until stiff peaks form.
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Add breadcrumbs, cinnamon, rum and vanilla extract to the apples.
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Carefully and slowly add the egg whites to the apples and pour the mixture to the bottom dough.
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Cover the filling with the ribbons, egg wash them and put the skillet to bake for 35 - 40 minutes.