Preheat oven to 375 degrees F. Line a baking sheet with parchment paper or a silicon baking sheet.
Put the unsweetened and semisweet 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 an inch 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.)
Whisk the sugar, eggs and vanilla into the chocolate mixture until smooth.
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.
Use a small cookie scoop or spoon to drop a heaping tablespoon of batter onto the prepared pan. Repeat to make 36 cookies, spacing them about 1-inch apart. Bake until the cookies spring back when lightly touched, about 6 minutes.
Cool the cookies slightly. Transfer half of the cookies to a rack. Turn the remaining cookies on the pan over, so they lay flat side up. Place a marshmallow on top of each flipped cookie and return pan to the oven. Cook just until the marshmallow begins to soften and puff, about 3 minutes. Cool marshmallow topped cookies slightly, about 2 minutes. Top with the remaining cookies, pressing lightly to make sandwiches. Cool whoopee pies completely on wire racks. Serve.
Store in tightly sealed container for up to 1 week.