Preheat the oven to 325 degrees F. Line two baking sheets with parchment paper.
Beat the butter, powdered sugar, and granulated sugar in the bowl of a stand mixer for 2-3 minutes until creamy and light. Add the eggs, egg white, and vanilla extract, then beat again, scraping the bottom and sides of the bowl.
Add the flour and salt, mixing just until combined.
Transfer the dough to a piping bag fitted with a 1/2-inch round piping tip. Pipe 2-inch lines a couple inches apart on the parchment paper-lined baking sheets, leaving enough room for the cookies to spread a bit in the oven. Bake for 13-15 minutes just until the edges are golden brown. Remove the cookies and cool completely.
Meanwhile, melt the chopped chocolate in a glass bowl set over, but not touching, simmering water in a pan, or in the microwave using short 20 second bursts of heat until melted and smooth.
Gently spread some of the melted chocolate onto the bottom side of half of the cookies, then sandwich with another cookie on top. The melted chocolate will firm up and set as it cools.
Store in an airtight container on the counter for up to 5 days.