For the pie crust
Place all of the ingredients for the crust, except the water, in a bowl and put in the freezer for 10 minutes.
After 10 minutes, remove from the freezer and transfer to the bowl of a food processor. Pulse a few times until the butter is broken up and the mixture is a mealy texture. While pulsing, pour in the water one tablespoon at a time. Pulse just until the dough starts to come together into a ball. Turn the dough out onto a floured surface. Shape into a disk, wrap in plastic and refrigerate for an hour.
Preheat oven to 375 F. Remove the dough from the refrigerator onto a floured work surface. Roll into a circle just large enough to fit the pie dish. Fit it into the dish and crimp the edges. Return the crust to the freezer for 10 minutes.
After 10 minutes, remove the crust from the freezer and line with a square of parchment paper large enough to hang over the edges. Fill with pie weights or dried beans. Bake 20 minutes. When the edges begin to turn slightly golden, remove the pie weights and parchment paper. Continue to bake 8-10 more minutes. Remove from oven and set aside.
For the crumb topping
Melt the butter and let it cool slightly.
In a medium bowl, combine the dry ingredients with a fork. Slowly drizzle in the butter and mix until it becomes a crumbly texture. Set aside.
For the caramel
In a small saucepan set over medium-high heat, combine water and sugar. Heat until the sugar dissolves and the mixture is boiling. Add the butter and continue to cook until it becomes golden brown. Be careful not to burn.
Remove from heat. Carefully pour in room temperature cream (it will sputter and bubble). Whisk until smooth and set aside. If it hardens, return to low heat and stir until smooth.
Toss the chopped apples with sugar, flour and cinnamon. Spread a third of the apples in the bottom of the pie shell. Drizzle with a third of the caramel, then nestle the pie bird in the center of the pie. Add the next third of the apples and caramel. Finish with the last third of the apples and cover with the crumb topping. Reserve the last of the caramel for serving.
Bake 40-50 minutes at 375 F. Let cool at least one hour before serving. Serve with the remaining caramel drizzled on top.