Preheat oven to 190C/Gas 5.
1) Line a baking tray with greaseproof paper or a silicon baking mat.
2) Put the plain and milk chocolates and butter in a medium microwave-safe bowl. Heat at 75 percent power until softened, about 2 minutes. Stir, and continue to microwave until completely melted, about 2 minutes more. (Alternatively, put the chocolate and butter in a heatproof bowl. Bring a saucepan filled with 2cm or so of water to a very slow simmer; set the bowl over, but not touching the water, and stir occasionally until melted and smooth.)
3) Whisk the sugar, eggs and vanilla into the chocolate mixture until smooth.
4) Sift the flour, cocoa, baking powder and salt into another bowl. Gradually whisk the dry ingredients into the wet ingredients until moistened. Switch to a rubber spatula and finish folding the batter together; take care not to over-mix.
5) Use a small biscuit scoop or spoon to drop a heaping tablespoon of batter onto the prepared pan. Repeat to make 36 biscuits, spacing them about 2.5cm apart. Bake until the biscuits spring back when lightly touched, about 6 minutes.
6) Cool the cookies slightly. Transfer half of the biscuits to a rack. Turn the remaining biscuits on the pan over, so they lay flat side up. Place a marshmallow on top of each biscuit and return pan to the oven. Cook just until the marshmallow begins to soften and puff, about 3 minutes.
7) Cool marshmallow topped biscuits slightly, about 2 minutes. Top with the remaining biscuits, pressing lightly to make sandwiches.
8) Cool whoopee pies completely on wire racks. Serve.
Store in tightly sealed container for up to 1 week.