For the Cookie: Preheat your oven to 325 degrees. Line two baking sheets with parchment paper.
Whisk together the flour, cocoa powder, salt, and baking soda in a medium bowl. Set aside.
Cream together the soft butter with both sugars until fluffy. Slowly whisk in the vanilla and melted chocolate and mix until fully combined. Stir in the egg.
Fold in the dry ingredients until incorporated.
Turn the dough out onto a lightly floured surface. Roll ¼ inch thick and cut into circles. Place on your prepared trays and bake 12-14 minutes or until the edges are slightly curled. Cool completely.
For the filling: Beat your butter with an electric mixer until fluffy. Slowly incorporate the powdered sugar, vanilla, milk, and salt. Whisk until light and fluffy. Spread 1-2 teaspoons of frosting onto one cookie. Push a second cookie down to sandwich and enjoy.