Preheat oven to 350 degrees F (175 degrees C). Place the pie crusts in 3 pie pans, and set aside.
Beat together the eggs, sugar, melted butter, flour, and vanilla extract in a bowl until smooth, and stir in 1 cup of cream. Pour the mixture in equal amounts into the pie crusts.
Bake in the preheated oven until the filling has set, about 35 minutes. Let the pies cool, and trim off the excess pie crust down to the top of the filling.
Place the brown sugar, 1 cup of cream, and 1/2 cup of sugar in a heavy saucepan over medium-low heat, bring to a boil, and cook, stirring constantly to prevent burning, until a candy thermometer reads 140 degrees F/60 degrees C, or until a small amount of syrup dropped into cold water forms a soft ball that flattens when removed from the water and placed on a flat surface.
Remove from the heat, and beat the mixture with a wooden spoon until thickened and cool. Stir in the butter and vanilla extract, and continue beating until the butter is incorporated, about 5 minutes. The icing should be thin and smooth, like a glaze.
Spread a thin layer of the caramel glaze on top of each pie, and firmly stack the pies together. Glaze the edges of the stacked pie.