2 c  All purpose flour
1/4 c  Plus
3 tb Unsweetened cocoa powder
1/4 ts Baking powder
1/4 ts Salt
1    Stick plus
3 tb Unsalted butter; at room
-temp
3/4 c  Sugar
1    Egg
1 ts Vanilla extract
2    -(up to)
2 1/2 pt Vanilla or coffee ice cream

Preheat oven to 350F. Line a 10 1/2 by 15 1/2 inch jellyroll pan with
parchment paper or aluminum foil with the dull side up, pressing it along
the edge and leaving an overhang on all sides. Butter the paper. Sift
together the flour, cocoa, baking powder and salt.

In an electric mixer, beat the butter at moderately high speed until light
and creamy. Scrape down the sides of the bowl. With the mixer on,
gradually add the sugar; scrape down the sides of the bowl. Add the egg and
vanilla and beat until well blended. Reduce the speed to very low and add
the flour mixture. Mix until just barely blended; do not overmix. Turn off
the machine and finish mixing by hand with a large rubber spatula (the
dough should ahve the consistency of modeling clay; if too dry, add a few
drops of cold water).

Transfer the dough to the prepared pan. Unsing your fingers, press the
dough over the bottom of the pan to an even thickness. With a toothpick,
make holes in the dough at 1/2 in intervals.

Bake until the cookie is set and the surface looks slightly dry, 8 to 9
minutes. Do not overbake, or it will be brittle. Transfer the pan to a
wire rack. Cut the cookie in half crosswise while it is still hot, then let
cool completely.

Place the ice cream in the refrigerator to soften until spreadable, about
10 minutes. Holding the edges of the parchment paper, lift off the cookie
and place it on a work surface. Place a clean sheet of foil in the baking
pan. With two spatulas, carefully transfer one of the cookie halves to the
foil. Gently spread the ice cream over this half of the cookie in an even
layer 3/4 inch thick, leaving a narrow border on all sides. With two
spatulas, carefully set the second cookie on top and press very gently into
place. Smooth the sides. Cover the sandwich wtih plastic wrap and freeze
until the ice cream is hard, about 2 hours.

Remove the sandwich from the freezer and let stand for about 5 minutes to
make it easier to cut. Dip a large chefs knife in hot water, wipe dry and
cut the sandwich into 6 even rectangles. If you are not serving them
immediately, wrap each sandwich individually in plastic wrap and store in
the freezer for up to a week.