Preheat oven to 375 degrees F.
To make the Dough: In a mixer fitted with the paddle attachment, cream the butter until soft and smooth. Add the sugar and continue mixing until well blended. Add the vanilla and mix until light and fluffy.
In a separate bowl, stir together the cocoa powder, cornstarch and flour. With the mixer running at low speed, add the dry ingredients to the butter mixture and blend just until combined. Form the dough into a disk, wrap it in plastic wrap and chill at least 2 hours or overnight.
On a floured work surface, using a floured rolling pin, roll the dough out to 1/8-inch thick, or as thin as you can possibly get it. Use flour-dipped cookie cutters to cut out 1 1/2 inch diameter circles and place them on an ungreased sheet pan, leaving 1-inch between the cookies. You can re-roll the scraps. To make them look more like store bought, prick the disks with a fork a little. Bake until crisp, 12 to 14 minutes, then let cool on the pan
To make the Marshmallows: Combine the 1/4 cup water, the corn syrup, and the sugar in a saucepan fitted with a candy thermometer. Bring to a boil and cook to "soft-ball" stage, or about 235 degrees F.
Meanwhile, in a standing mixer fitted with a whisk, whip the egg whites until soft peaks form. Sprinkle the gelatin over the 2 tablespoons water and let dissolve. When the syrup reaches 235 degrees F, remove it from the heat, add the gelatin, and mix. Pour the syrup into the whipped egg whites. Add the vanilla and continue whipping until stiff.
Transfer the mixture to a pastry bag fitted with a round tip. Pipe a "kiss" of marshmallow onto half of the cookies, and top with the rest to make sandwiches. Let set at room temperature for 2 hours.
To make the Chocolate Coating: Melt the 2 ingredients together in the top of a double boiler or a bowl set over barely simmering water, stirring occasionally. Line a cookie sheet with parchment paper or a nonstick baking mat. One at a time, gently drop the marshmallow-filled cookies into the hot chocolate. Lift out with a fork and let the excess chocolate drip back into the bowl. Place on the cookie sheet and let set at room temperature until the coating is firm, about 1 to 2 hours.