Preheat your oven to 375F

Whisk the egg and vanilla in a small cup and set aside.

Pulse the dry ingredients in the bowl of a food processor to combine.  Drop in the pieces of butter and pulse until the butter is incorporated and the mixture is crumbly.

Pour in the egg mixture and pulse again, about 25 or 30 times, until the dough comes together.

Turn out the dough onto a floured surface and bring it together in a ball.  Divide in 2.  Roll out each half into a log about 1 1/2 inches in diameter.  The log will be approximately 6 inches or so long.

Roll the logs in plastic wrap, and refrigerate for about an hour.  I like to put my dough logs inside a split cardboard tube (like the kind that wrapping paper comes on) so that the log stays nice and round.  If you don't have one, try turning and reshaping your dough halfway through the chilling time.

Slice the chilled logs of dough into 1/8 inch slices, and place them 1 inch apart on ungreased cookie sheets.

Bake at 375 for about 8 to 10 minutes, until just golden around the edges.  Cool on a rack.

Mix the peanut butter, the sugar and the vanilla.  Spread an even layer of the filling on each cooled cookie.

Put the chocolate into a 2 cup Pyrex measuring cup, and microwave for 1 minute.  Take out and stir.  If the chocolate is not completely melted, microwave for another 30 seconds.  Stir until completely melted and smooth.  Make sure you measuring cup is completely dry, even a drop of water will cause your chocolate to seize up.

Take a cookie and spread chocolate across the bottom.  A small offset spatula works well for this.  Then place the cookie on a fork, and spoon the melted chocolate all over the top, being sure to cover the whole top.  Tap the fork along the edge of the bowl to remove the excess chocolate from the cookie.  Carefully lay the cookie on waxed or parchment paper.

If your chocolate becomes too thick to work with, microwave it for 15 to 30 seconds to-re warm it.

Let all the cookies set for 30-45 minutes or so until the chocolate firms up.  Store in the refrigerator in an airtight container until ready to eat.