Let ice cream stand at room temperature until slightly softened, about 15 minutes. Place ice cream and peanut butter cups in a large mixing bowl and stir with a wooden spoon until well combined. Transfer ice cream mixture to prepared crust and smooth with back of wooden spoon. Place pie in freezer.
Combine heavy cream, sugar and vanilla in a large bowl and whip with an electric mixer on medium-high speed until cream holds soft peaks.
Remove pie from freezer and smooth whipped cream over ice cream. Freeze until whipped cream is firm, then cover lightly with plastic wrap and freeze until pie is firm, at least 3 hours and up to 1 week.
To serve, let pie stand on counter to soften for 5 to 10 minutes before slicing. Serve with hot fudge sauce on side, if desired.