Make the crepes: Combine the milk, eggs, flour, cocoa powder, granulated sugar, vanilla and salt in a blender and process until smooth. Refrigerate the batter 30 minutes.
Lightly brush a 10-inch nonstick skillet with melted butter and place over medium heat. Add a scant 1/4 cup of batter and quickly swirl the pan to coat the bottom. Cook until set on top and golden on the bottom, about 30 seconds. Carefully lift the edge of the crepe with a rubber spatula, then flip with your fingers and cook 20 more seconds. Invert the crepe onto a plate. Repeat with the remaining batter to make 14 to 18 crepes, brushing the skillet with more butter as needed. Stack the finished crepes on the plate and let cool completely. (The crepes can be made up to 1 day ahead; let cool, then wrap the stack in plastic wrap and refrigerate.)
Make the filling: Beat the butter in a stand mixer fitted with the paddle attachment on medium-high speed until light and fluffy. Add 2 3/4 cups confectioners' sugar in 2 batches, beating until smooth and fluffy. Add the dulce de leche and beat until combined. (The filling can be made up to 1 day ahead; cover with plastic wrap and refrigerate, then beat for a few minutes with a mixer before using.)
Assemble the cake just before serving: Place 1 crepe on a platter or cake stand. Spread with a scant 1/4 cup of the filling, then top with another crepe. Repeat with the remaining filling and crepes, ending with a crepe on top.
Beat the heavy cream and the remaining 1 tablespoon confectioners' sugar in a stand mixer fitted with the whisk attachment until stiff peaks form. Spread on top of the cake and drizzle with dulce de leche. Serve immediately.