In a mixing bowl, combine chocolate cookie crumbs with melted butter, stirring until the mixture resembles wet sand. Firmly press this mixture into the bottom of a springform or lined pan, ensuring an even layer. Place the crust in the freezer for about 30 minutes, or until set and firm to the touch.

In a small saucepan, bring sugar and water to a gentle simmer over medium heat, stirring for about 2 minutes until the sugar completely dissolves. Once dissolved, remove from heat and add in chopped dark chocolate. Stir until completely smooth. Allow the mixture to cool to room temperature.

In a separate mixing bowl, use an electric mixer to beat heavy cream until soft peaks form. Add mascarpone cheese to the whipped cream and continue beating until thick and creamy. Carefully incorporate the cooled chocolate mixture into this whipped cream mixture, folding gently until fully combined and smooth.

Once the chocolate filling is prepared, pour it over the chilled crust you made earlier. Use a spatula to smooth the top for an even finish. Cover the pie tightly with plastic wrap and freeze it for at least 8 hours or overnight.

Before serving your Creamy Frozen Chocolate Pie, let it sit at room temperature for about 10-30 minutes to soften slightly for easier slicing. When ready, cut the pie into slices and top each piece with dollops of whipped cream and a sprinkle of grated chocolate.