Making the crust: Place the ginger snap cookies in a food processor and pulse to grind them into fine crumbs. While the food processor is running, drizzle in the 4 tablespoons melted butter, 1 tablespoon granulated/cane sugar and kosher salt. Mix just until fully combined. Press evenly into the bottom of a 9-inch diameter 3-inch high (12 cup volume) spring form pan. Cover with plastic wrap and place in the freezer to set (about 1 hour).
Making the Cinnamon Ripple: Melt 4 tablespoons of the remaining butter in a small sauce pan over medium-high heat. Stir in ¼ cup light brown sugar, ¼ cup granulated/cane sugar, and cinnamon; lower the heat to medium and stir to combine. As the sugar begins to melt, add ¼ cup of the heavy cream and stir to dissolve the sugar fully. Remove from heat and allow to cool to room temperature (may be placed in the refrigerator to hasten cooling; do not allow to over thicken).
In the bowl of a standing mixer equipped with the paddle attachment, cream the cream cheese. Add the pumpkin, pumpkin pie spice and the remaining 1/3 cup of light brown sugar; beat on high to fully combine.
Spoon the ice cream into the bowl and mix in on the lowest speed until all ingredients are fully combined (don’t worry if ice cream becomes very soft). Spoon half the mixture into the 9-inch spring form pan with the frozen crust. Tap pan on the countertop a few times to release any air pockets. Drizzle half of the cooled Cinnamon Ripple on the top of the ice cream mixture. Drag a dining knife through the cinnamon ripple to mix into the ice cream mixture.
Repeat Step 4 with the remaining half of the ice cream mixture and the remaining cinnamon ripple. Smooth the top of the filling with a mixing spoon or spatula. Tent the top of the pan with foil (ensuring it does not touch the top of the pie filling), return to the freezer, (ensure it is on an even flat surface) to set fully (3-4 hours or overnight).
Making the Salted Caramel Sauce: In a medium saucepan over medium heat, melt the remaining 4 tablespoons of butter. Add the remaining ¼ cup granulated/cane sugar and the dark brown sugar to the melted butter and stir constantly until the mixture begins to simmer. Slowly pour in the remaining ½ cup heavy cream, stirring constantly. Allow the mixture to come to a simmer again and simmer for 3 minutes, stirring constantly. Remove from heat and stir in the sea salt. Allow to cool fully (may be stored sealed in the refrigerator).
To serve: remove pie from the freezer and allow to sit at room temperature for about 5 minutes until the spring form pan can be opened and removed. Place pie on a serving platter for slicing at the table or sliced onto individual plates. Drizzle with Salted Caramel Sauce and a dollop of whipped cream.