Preheat the oven to 450° F. Very lightly coat the bottom of an 8" x 8" pan with cooking spray.
Peel the sweet potatoes. Cut them into 1-inch thick slices and then cut each slice into quarters. Place the cut potatoes into the pan along with the boiled cider and 2 tablespoons of the brown sugar. Toss the potatoes to coat them with sugar and cider.
Cover the pan with foil and bake for 15 minutes. Remove the foil, stir the potatoes and bake them uncovered for 20 to 30 more minutes. The potatoes should be soft and mashable.
Remove the pan from the oven, transfer the potatoes to a dish and allow them to cool to room temperature.
Prebake the pie shell:
Use half of the Perfect All-Butter Pie Crust recipe - the dough should be chilled. Roll out the dough to ¼-inch thickness and cut out a circle large enough for the pie pan.
Fit the dough into the pan. Fold under and crimp the edges all around. Line the pie shell with foil and it should extend over the edges as well. Fill the shell with pie weights or dried beans.
Refrigerate the crust while you preheat the oven to 375° F.
Bake the shell for 20 minutes. Remove the pie weights and foil, then prick the shell all over with a fork. Bake the shell for 10 minutes longer. Let the shell cool while you make the filling.
Make the filling:
Purée the cooled sweet potatoes in a food processor while slowly adding in the half and half. The potato/half and half mixture should be as smooth as possible - purée it in batches if need be. Transfer the puréed potatoes to the bowl of a stand mixer.
Melt the remaining 3 tablespoons butter in the microwave (10 second bursts until it's melted.) Add this to the sweet potatoes. Add in the eggs, the remaining 2/3 cup of brown sugar, the granulated sugar, vanilla, cinnamon, nutmeg and salt.
Mix everything together in the stand mixer until the ingredients are combined and smooth.
Assemble the pie:
Reduce the oven heat to 350° F. Spoon the sweet potato filling into the prebaked shell and smooth the top. Cover the pie crust edges with foil to prevent over-browning.
Bake the pie for 50 to 55 minutes until a knife inserted in the center comes out almost clean. Allow the pie to cool completely on a cooling rack.
Fresh, sweetened whipped cream can be spread over the cooled pie before slicing, or simply add dollops to slices as you serve them. Spreading whipped cream over the uncut pie can be a great option to hide a crack in the top of your pie, should one appear after it's baked!
To make fresh, whipped cream:
Chill the bowl and whisk from your stand mixer in the freezer for 10 minutes, then assemble them on the mixer. Beat the heavy cream and confectioner's sugar for 4-5 minutes on high speed until stiff peaks form. Spoon the whipped cream over the pie before slicing it, or add dollops to individual slices. Serve the pie.