Preheat your oven to 325°F. Line a rimmed baking sheet with unbleached parchment paper and set it aside.
Make the cookies.
In a large bowl, place the flour, xanthan gum, salt and sugar, and whisk to combine well. Add the butter, vanilla, and 1 tablespoon water, and mix to combine.
Knead the dough with your hands to bring it together. If necessary for the dough to hold together, add another tablespoon of water, 1 teaspoon at a time.
Press the dough into a disk, and then place the disk between two sheets of unbleached parchment paper and roll the dough between 1/8 inch and 1/4 inch thick.
Cut out 2-inch rounds with a cookie cutter. Gather, reroll and cut any scraps into rounds.
Transfer the cookies carefully to the prepared baking sheet by peeling back the parchment paper from the bottoms of the cookies.
Place the cookies in the center of the preheated oven and bake until the cookies are set and just beginning to brown around the edges (about 8 minutes).
As soon as the cookies come out of the oven, press your thumb or the bowl of a small spoon into the center to create a well for the filling.
Allow the cookies to cool for a few minutes on the baking sheet until they are firm enough to transfer to a wire rack to cool completely.
Make the filling.
While the cookies are cooling, place the peanut butter and melted coconut oil, vanilla and salt in a large bowl and mix to combine. Add the confectioners’ sugar, and stir until well-combined. The mixture will be very thick.
Add one tablespoon of water, and stir to thin the filling. Add another teaspoonful of water if necessary to create a thickly pourable filling.
Allow the filling to cool until no longer hot to the touch.
Assemble the cookies.
Place the cooled cookies on the prepared baking sheet in a single layer.
Place the filling in a pastry bag fitted with a medium-sized plain tip (I used a #12 tip) or a ziptop bag with the corner cut off. Pipe a generous amount of filling on top of each cooled cookie, leaving at least a 1/2 inch border around the perimeter of the cookie.
With wet fingers, press down the filling. Place the cookies in the freezer until the filling is well-chilled (about 5 minutes).
Make the chocolate topping & finish the cookies.
Melt the chocolate and shortening in a double boiler or a small, microwave-safe bowl, on 70% power at 30-second intervals, stirring in between, just until melted and smooth.
Remove the chilled cookies from the freezer, and carefully immerse each cookie in the melted chocolate.
With a dipping fork (or any fork, really), carefully turn the cookie over in the chocolate until it is completely coated. Turn the cookie right side up in the chocolate and draw the cookie out of the chocolate on the tines of the fork, scraping the bottom of the fork on the side of the bowl to rid the bottom of excess chocolate.
Place the cookie back on the parchment paper.
Allow the cookies sit at room temperature until the chocolate is set.
Store in an airtight container in the refrigerator until ready to serve. Freeze any leftovers.