Pulse the Oreo cookies (with the cream removed) in a food processor until they are fine crumbs. If you don’t have a processor, place cookies in a zip-top bag and crush with a rolling pin until evenly ground.
Combine the Oreo crumbs and melted butter in a bowl and stir until the crumbs are evenly moistened. Transfer the mixture into a 9-inch springform pan and press firmly and evenly across the bottom using the back of a measuring cup. Refrigerate the crust for 20–30 minutes to set while you prepare sauces.
Make the chocolate sauce: in a small heavy saucepan over low heat, whisk the sugar, cream and butter until warm and the sugar dissolves. Add the chocolate chips and stir constantly until smooth and glossy. Remove from heat and stir in the vanilla. Allow to cool to room temperature, then refrigerate briefly if it needs to thicken before serving.
Make the caramel sauce: in a clean saucepan over medium heat, cook the sugar without stirring until it melts and turns a deep amber (tip the pan gently to help it color if needed). Remove from heat and quickly whisk in the butter, then very carefully add the cream (mixture will bubble). Stir until smooth and finish with a small pinch of flaky sea salt if desired. Set aside to cool.
Toast the sliced almonds in a dry skillet over medium heat, shaking the pan, until fragrant and lightly browned, 3–4 minutes. Transfer to a plate to stop cooking.
Let the ice cream sit at room temperature for 8–10 minutes so it softens. Stir in the instant espresso powder, if using, to sharpen the coffee notes. Spoon the softened ice cream over the chilled Oreo crust and smooth into an even layer. Sprinkle the toasted almonds across the top.
Cover the pan with plastic wrap and freeze the assembled pie for at least 8 hours or overnight until solid.
To serve, remove the pie from the freezer and run a thin-bladed knife under hot water, wipe dry, then use it to slice the pie. Warm the chocolate and caramel sauces gently in the microwave for 10–20 seconds or in a small saucepan just until pourable, and drizzle over slices right before serving.
Store leftovers in an airtight container in the freezer. Let slices sit 3–5 minutes at room temperature before eating for a softer texture.