For the brownies: Preheat the oven to 350 degrees F. Grease the bottom of a jellyroll pan, then line with parchment paper and grease the paper.
In a microwave-safe bowl, melt the shortening and chocolate together, stirring every 30 seconds and cooking until melted. Set aside to cool slightly.
In the bowl of a stand mixer fitted with the paddle attachment, beat the eggs well. Add the granulated sugar and vanilla; beat to combine thoroughly. Beat in the chocolate mixture.
In a medium bowl, whisk together the flour, baking powder and salt. Stir into the chocolate mixture. Spread the batter evenly in the prepared pan.
Bake the brownies until a toothpick inserted in the center comes out clean, 12 to 15 minutes. Remove from the oven and let cool in the pan for 10 minutes. Release the edges with a butter knife, and turn the brownies out onto a cutting board to cool completely. Cut in half, creating two large, equal pieces.
For the filling: In the bowl of a stand mixer fitted with the paddle attachment, combine the shortening and vanilla. Add the confectioners' sugar, 1 cup at a time, adding 1 tablespoon of water between each addition and mixing until you get a spreadable consistency. You may not need to add all the water.
Spread the filling over one of the large brownie pieces, and cover with the other piece like a sandwich. Cut into 2-inch" squares.
These are SO good. You can also halve the brownie recipe and make a thinner cookie; you'll need to reduce the baking time to 8 to10 minutes. (Though my crowd likes the brownie-to-filling ratio in this recipe.)