Peel and slice the apples. Heat the butter in a wide pot over medium-high heat. Add the apples along with the sugar, cinnamon, nutmeg, allspice, salt, and lemon juice. Stir to combine.

Cook the apples, stirring occasionally, just until they are softened and begin to release their juices. Transfer the apples and their juices to a wide dish, spread them out to cool, and transfer to the fridge after cooling slightly.

Make the dough in a food processor. Add the flour and salt and pulse to combine. Add the cold, diced butter and pulse until the mixture resembles small peas.

Pour the ice water into the food processor while pulsing until the dough begins to stick together. Shape the dough into a ball, cut into two pieces, and chill for at least 1 hour.

Melt the butter in a small saucepan over medium heat. Add the brown sugar and whisk together. Add the heavy cream and whisk until emulsified. Bring the sauce to a boil and cook for 1 to 2 minutes. Let cool before using.

Preheat the oven to 350?F. Lightly grease a pie plate.

Roll out the larger disc of dough on a floured surface into a circle about 2 inches larger than the pie plate. Place the dough in the pie plate.

Prepare an egg wash by whisking the egg with the water. Add cornstarch to the cooled apple mixture and mix well. Spoon half of the apple mixture into the pie crust and drizzle with half of the toffee sauce. Repeat with the remaining apple mixture and toffee sauce.

Roll out the remaining disc of dough into a circle slightly larger than the pie plate. Brush the edges of the bottom crust with the egg wash.

Cut the top dough into 10 strips and create a lattice over the filling, trimming excess dough and crimping the edges.

Brush the top with the egg wash. Bake for 50 to 60 minutes or until bubbling and browned. Let cool before slicing.

For the custard sauce, whisk together the egg yolks, sugar, cornstarch, and salt in a bowl. Heat the milk and temper it into the yolk mixture. Return to heat and cook until just boiling, then stir in butter and vanilla. Strain and let cool.