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Preheat the oven to 325°F, and line two baking sheets with parchment.
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For the cookies: In a small bowl, whisk together the flour, cocoa powder, and salt.
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Beat together the butter and brown sugar until light and fluffy. Mix in the extracts. Slowly add the dry ingredients and beat until just combined. The dough will be a bit crumbly.
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Pour the mixture onto your work surface and give it a few kneads to bring it together. Dust your surface with cocoa powder, roll out your dough, and cut out 2" circles.
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Transfer the cookies to your baking sheets, spacing them about 1" apart. Re-roll the scraps and cut circles until all of the dough is used up. Bake the cookies for 18 to 20 minutes, or until the tops are no longer shiny. Remove them from the oven and cool on a rack.
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For the marshmallow filling: Place the gelatin and 5 tablespoons of the water in the bowl of a stand mixer fitted with a whisk attachment and stir to combine.
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Combine the sugar and the remaining 4 tablespoons of water in a small saucepan. Insert a candy thermometer, bring to a boil over medium heat, and cook to soft-ball stage (235°F).
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Remove the pan from the heat and gradually pour the syrup into the gelatin mixture with the mixer on low. Once the mixture is combined and no lumps remain, increase the mixer to medium speed.
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Once the marshmallow has turned white and opaque, add the peppermint extract and turn the mixer to high speed. Beat for 10 minutes, until the marshmallow is stiff, glossy, and white.
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To assemble the cookies: Use a greased rubber spatula to fill a piping bag with the filling, and pipe a blob onto the center of half of the cookies. Top with the rest of the cookies to make sandwiches.
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Place cookies in the refrigerator for a few minutes to let the filling firm up before serving. Store any leftovers in the fridge.
