Preheat oven to 325°. Butter and lightly flour a sturdy 9-in. metal pie pan to keep crust from sticking. In a food processor, grind cookies with sugar into fine crumbs. With motor running, drizzle in 4 tbsp. butter and whirl, scraping bottom of bowl occasionally, until crumbs come together (you may have to drizzle in more butter).
Press crumb mixture evenly and firmly over bottom, up sides, and slightly higher than rim of pie pan (don't press onto the rim, or it will crumble when cut). Press rim firmly together so it's not crumbly. Run a spoon around bottom inner edge of pie, scooping away extra crumbs; otherwise it tends to get too thick and clunky.
Bake crust 12 to 14 minutes, or until crust is firm and lightly toasted. Let cool completely.
In a large mixing bowl, mash ice cream to an even consistency with a metal pastry blender or large fork. Mix in crushed toffee.
Carefully dollop ice cream into center of cooled crust and spread outward, not quite but almost to edge (the ice cream will naturally settle outward to fill the crust). With a small metal spatula, smooth the top flat. Slide into freezer, making sure the pie is level (otherwise it will freeze lopsided). Freeze until firm to the touch, at least 2 hours, then smooth on the thinnest possible layer of chocolate ganache. Sprinkle pie with toasted almonds; then freeze at least 2 hours more and up to 1 week.
Let sit at room temperature 5 to 10 minutes before slicing.
*Find crunchy, very almondy Italian amaretti in well-stocked grocery stores. Or use almond biscotti instead and whirl in 1 tsp. almond extract with the melted butter.
Make ahead: Pie, up to 1 week, loosely covered with plastic wrap and frozen.