Remove cones from freezer, then wrap each one with a parchment quarter, securing with a piece of tape (see photos above).
Working one at a time, use a small spoon to scoop the ice cream into a cone, filling almost to the top of the parchment paper. Immediately return to the freezer, and repeat with the rest of the cones. Allow cones to chill in the freezer for at least 2 hours.
If melted chocolate has hardened, re-melt it in the microwave at 30-second increments until smooth. If possible, pour melted chocolate into a smaller, flat-bottomed bowl to make dipping easier. Place toffee bits into a small bowl.
Again, working one at a time, remove a cone from the freezer, dip the top of the cone into the chocolate. Allow excess chocolate to drip off, then immediately dip (or sprinkle) in toffee bits. Return to the freezer and repeat process with the rest of the cones. Keep in the freezer until ready to serve.