How to Make It
Make the cookies: Heat oven to 350° F. Line 2 baking sheets with parchment. Whisk together the flour, cocoa, baking powder, and salt in a bowl.
Combine the chopped chocolate and butter in a microwave-safe bowl. Microwave on high in 30-second intervals, whisking in between, until melted and smooth. Let cool slightly. Whisk in the sugar, eggs, milk, ginger, and vanilla until smooth. Add the flour mixture; stir until just combined. Fold in the chocolate chips.
Shape the dough into balls (about 1 tablespoon each) and place 1 inch apart on the baking sheets. Bake, rotating the sheets halfway though, until golden brown around the edges, 8 to 10 minutes. Let cool slightly on the baking sheets, then transfer to a wire rack to cool completely.
Make the filling and assemble the sandwiches: Bring the cream to a boil in a small pot. Remove from heat, add the chocolate, and let sit for 5 minutes. Whisk to combine. Let cool slightly. Form sandwiches with the cookies and about 1 teaspoon filling each.