Preheat the oven to 325 degrees. Line baking sheets with parchment paper.
Place the chocolate chips in a microwave-safe bowl and microwave on high for 1-2 minutes or until melted, stirring every 30 seconds. Add the shortening and stir until melted. Let cool while the cookies bake and cool.
In the bowl of an electric mixer fitted with a whisk attachment, beat the egg whites and salt on high speed until stiff peaks form. Add the sugar gradually and continue beating until the egg whites are very thick, 2-3 more minutes. Beat in the vanilla. Stir in the almond meal using a large spatula, making sure to fully combine. The batter will be very thick and sticky.
Using a small ice cream scoop or a tablespoon, drop mounds of the dough onto the prepared baking sheets, spacing about 2 inches apart.
Bake for 15-17 minutes, rotating the pans halfway through, or until the cookies are set and slightly cracked. Let cool on the baking sheets for 5 minutes, then transfer the cookies on the parchment paper to a wire rack to finish cooling completely, at least 30 minutes.
Spoon some of the chocolate filling onto the flat side of one cookie, place another cookie flat side down on the chocolate, and gently press the cookies together. Repeat with the remaining cookies and filling.
Notes
These cookies do not brown much and might not look "done" but if you follow the cooking time, they are done! They will harden slightly as they cool, so do not over-bake them.