Line an 8-quart bowl with overhanging plastic wrap.
Tip the coffee ice cream into the bowl and smooth the surface. Sprinkle over the chopped pecans and freeze until the ice cream is firm, at least 1 hour.
Tip the chocolate ice cream into the bowl and smooth the surface. Sprinkle over the chocolate-coated toffee pieces and freeze until firm, at least 1 hour.
Meanwhile, make the crust: Put the sandwich cookies in a food processor and pulse until fine crumbs. Pour in the melted butter and pulse to combine.
Tip the vanilla ice cream into the bowl and smooth the surface. Tip the crust on top of the vanilla ice cream, spread it evenly and press down firmly. Freeze again until completely set, 4 hours and up to overnight.
Turn out the pie onto a board or serving platter lined with 4 squares of parchment arranged so that the paper overhangs the edges of the platter. Peel off the plastic wrap and pour over the chocolate shell ice cream sauce to coat the entire pie. Carefully slide out the sheets of parchment and discard.
To serve, cut big slices of pie, drizzle over some warm caramel sauce and stick a steak knife into the center standing up.