You will need 2 cookie sheets or jelly-roll pans lined with parchment or foil.
To make the dough, beat the butter by hand in a medium bowl just until it is evenly softened. Quickly beat in the melted chocolate, then the flour. Continue to mix until the dough is smooth.
Scrape the dough out onto a piece of plastic wrap and press it into a rectangle about 1/2-inch thick. Wrap and chill the dough until it is firm -- about an hour.
While the dough is chilling, make the filling. Combine the cream, butter and corn syrup in a saucepan and bring to a boil over low heat. Remove from heat and add both chocolates. Shake the pan gently to submerge chocolate in the hot liquid. Let stand 5 minutes, then whisk smooth and scrape filling into a bowl. Let stand at room temperature or in the refrigerator until of spreading consistency.
To bake the cookie bases, set racks in the upper and lower thirds of the oven and preheat to 350 degrees.
If the dough is very hard, pound it gently with the rolling pin to soften it so that it rolls out more easily. Divide dough in half and, on a floured surface, roll one half about 1/16-inch thick. Use a fluted, round 2-inch cutter to cut the dough into cookies. Place them on prepared pans as they are cut, leaving about an inch between the cookies. Repeat with the remaining dough. Save all the scraps. Reroll the scraps and cut more cookies.
Bake the cookies 12 to 15 minutes, until they are firm and slightly colored. Cool the cookies in the pans on racks.
When cookies and filling have cooled, arrange half the cookies, flat side up. Place a dab of filling on them and cover with the remaining cookies, flat sides together. Dust cookies very lightly with confectioners' sugar before serving