Line an 8-quart bowl with plastic wrap, leaving an overhang. Tip the coffee ice cream into the bowl and smooth the surface. Sprinkle the chopped pecans on top and freeze until the ice cream is firm, at least 1 hour.
Tip the chocolate ice cream into the bowl over the pecans and smooth the surface. Sprinkle the toffee pieces on top and freeze until firm, at least 1 hour.
Meanwhile, put the sandwich cookies in a food processor and pulse into fine crumbs. Pour in the melted butter and pulse to combine. Set aside.
Once the chocolate ice cream is firm, tip the vanilla ice cream into the bowl over the toffee pieces and smooth the surface. Tip the cookie mixture on top of the vanilla ice cream; spread it evenly and press down firmly. Cover with the overhanging plastic and freeze until completely firm, at least 4 hours and up to overnight.
Turn out the pie onto a cake stand or platter lined with 4 squares of parchment so that the paper hangs over the edges of the platter. Peel off the plastic wrap from the pie and pour the chocolate shell over the ice cream to cover completely. Slide out the sheets of parchment.
For an extra-sweet treat, drizzle each slice with warm caramel sauce.