Pulse chocolate cookies in a food processor to form fine crumbs. Add melted butter and mix until fully combined.
Press the crust firmly into the bottom of a 9-inch springform pan. Chill in the freezer for 15 minutes.
In a bowl, whisk sweetened condensed milk, chopped chocolate, and vanilla extract until smooth. Pour this fudge layer over the crust and smooth the surface. Chill for 30 minutes.
Spoon whipped cream into 8 evenly spaced mounds on the fudge layer. Returning the bowl and spatula to the freezer for 5 minutes, then use 2 tablespoons cocoa powder and a spoon to create a zigzag design on the fudge surface.
Transfer pan to freezer and chill for 2 hours. Meanwhile, in a small saucepan, heat milk and cocoa powder until just simmering. Pour over prepared popsicle sticks and let set into thin discs, about 10 minutes.
Once fudge is set, run a thin knife around the edges of the pan. Cut the pie into 8 equal wedges. Insert chocolate-coated sticks into the whipped cream mounds. Return to the freezer for 20 minutes before serving.