Make the compote: Combine the cranberries, brown sugar, and orange zest and juice in a heavy-bottomed saucepan. Cook over low to medium heat until the cranberries begin to burst. Remove from the heat and set aside to cool completely.

Make the crumble: In a mixing bowl, combine the oats, brown sugar, flour, cinnamon, and salt. Place the butter in the bowl and coat on all sides with the flour mixture. Cut the butter into ½-inch cubes and work to break up the cubes with your hands until they are lightly coated with the flour mixture. Use a pastry blender to cut in the butter until it is no longer visible.

Preheat your oven to 350°F. Line a baking sheet with parchment paper.

Make the filling: In a mixing bowl, combine the sugar, cinnamon, nutmeg, allspice, tapioca starch, and salt. Add the cranberries, pear, and cooled compote and mix completely.

Assemble and bake the pie: Spread the cream cheese on the bottom of the pie shell. Brush the crimped edge with the beaten egg. Layer the cranberry mixture on top of cream cheese and cover with the crumble topping, leaving a small hole in the center.

Place the assembled pie on the parchment-lined baking sheet and bake for 60 to 70 minutes, until the pie juices are beginning to bubble and the crumble topping is a uniformly deep golden color.

Remove the baking sheet from the oven and transfer the pie to a wire rack to cool for 4 to 6 hours. Slice into 6 to 8 pieces and serve with vanilla ice cream.