Place an inverted baking sheet in the oven and preheat the oven to 350 degrees F.
Lightly flour your work surface. Roll each round of pie dough out to a 12-inch circle. Place 1 round of dough on one side of a baking sheet, allowing about 1 inch of excess dough to hang over each side. Repeat this process with another round of dough on the long side of the baking sheet, slightly overlapping the rounds. Cut the third round of dough in half. Use the halves to cover the remainder of the baking sheet, being sure to leave about 1 inch excess dough on all sides. Prick the dough with a fork and cover with parchment paper. Use cookie cutters to cut hearts out of the fourth round of dough. Place the hearts on top of the parchment paper. Place the baking sheet with the crust and hearts in the refrigerator to chill while preparing the filling.
To prepare the filling, place a stockpot over medium heat. Add the apples, butter, brown sugar, cardamom and salt. Cook until the sugar dissolves into the melted butter, creating a loose syrup, 5 to 7 minutes. Sprinkle in the cornstarch and bring to a simmer. Cook until slightly thickened, about 5 minutes more. Stir in the cranberry sauce and cook, stirring, until combined, about 2 minutes. Remove from the heat and stir in the dried cranberries and vanilla.
Remove the pie dough from the refrigerator. Lift off the sheet of parchment with the hearts on it and set aside. Pour the filling over the crust and spread into an even layer with a spatula. Lightly press the excess dough over the edges of the filling to create a rustic crust. Decorate the filling and crust with the hearts.
In a small mixing bowl, whisk the egg with 1 tablespoon water. Brush the egg mixture over the crust and hearts.
Place the pie on top of the preheated baking sheet and bake until the filling bubbles and the crust is golden brown, about 55 minutes. Allow to cool slightly before slicing.