For the cookies: Sift the flour, granulated sugar, cocoa powder and baking soda together in a medium mixing bowl and set aside. Whisk the butter, milk and egg yolk together in a separate bowl until uniform in color and texture. Add the butter mixture to the flour mixture and stir until it forms a dough. Divide the dough in half and place each half onto a sheet of plastic wrap or parchment paper. Form into two logs about 1 to 1 1/2 inches in diameter. Refrigerate for at least 4 hours to overnight.
Preheat the oven to 375 degrees F. Line 2 baking sheets with parchment paper.
Remove one dough log at a time from the refrigerator. Slice into 1/4-inch-thick slices and place onto the baking sheets. Bake until firm and set, 8 to 10 minutes. Set aside on a rack to cool. Repeat with the second log.
For the banana filling: Add the butter and shortening to a small bowl and beat with an electric mixer on medium speed until combined, about 1 1/2 minutes. Reduce the speed to low and add the confectioners' sugar in two batches. Add the extracts and mix until combined; set aside.
Slice the banana into 3 dozen 1/8-inch-thick slices.
To assemble the cookies: Place a heaping 1/2 teaspoon filling on each cookie. Place a banana slice on the filling, making sure it does not overlap the edge, and then cover with another cookie and press down gently.
For the bittersweet ganache: Pour a couple inches of water into the saucepan and heat over medium-low heat to just below a simmer. Put the chocolate and shortening in a metal bowl and place over the hot water to melt, stirring often. If the water starts to steam too much, remove the bowl from the pan to avoid scorching the chocolate. When fully melted, remove from the heat, leaving the bowl of chocolate over the water. Using two forks, dip the sandwich cookies into the melted chocolate, turning gently to coat, and remove to wax paper. Allow to sit at room temperature until the chocolate is completely set, at least 2 hours.