Preheat oven to 350F (177C) and prepare cookie sheets by lining with parchment paper.  Set aside.

Combine dark chocolate chips and butter pieces in a large microwave-safe bowl.  2 cups (340 g) dark chocolate chips, ½ cup (1 stick) (113 g) butter

Microwave for 30 seconds. Stir well, microwave for another 15 seconds and then stir well again. Repeat for 15 seconds until chocolate and butter are completely melted and well-combined.

Set aside and allow to cool (about 10 minutes).  Meanwhile, whisk together flour, espresso powder, baking powder, and salt.¾ cup (100 g) all-purpose flour, 2 teaspoons espresso powder, ½ teaspoon baking powder, ¼ teaspoon salt

In the bowl of a stand mixer fitted with a whisk attachment, combine eggs, egg white, sugar, and vanilla extract and gently stir together.1 ¼ cup (250 g) granulated sugar, 3 large eggs + 1 egg white, ½ teaspoon vanilla extract

Gradually turn stand mixer up to high speed and whisk for three minutes (mixture will be slightly lighter and thicker).  Add chocolate to mixture and use a spatula to stir together until evenly combined.

Stir in flour mixture (do not overmix).

Drop cookie dough by 1 ½ Tablespoon onto prepared cookie sheet, spacing at least 2" apart.

Bake on 350F (177C) for 10-12 minutes (tops should be set).  Allow cookies to cool completely before removing from cookie sheets and filling.

Vanilla CreamBeat softened butter with an electric mixer until creamed.  Gradually add sugar until completely combined.  ½ cup (1 stick) (113 g) unsalted butter, 2 cups powdered sugar

Beat in milk until frosting is smooth and silky2 teaspoons milk

Stir in vanilla extract and salt.  Use a spatula to scrape the frosting into a piping bag (I used one fitted with a Wilton 2D tip, but just using a Ziploc bag with a hole snipped out of one corner would work as well) and set aide.½ teaspoon vanilla extract, ⅛ teaspoon salt

Chocolate Espresso Frosting(you can use the scraped-clean bowl you just used for the vanilla frosting -- save a dish!)In a microwave-safe bowl, microwave chocolate chips at 15 second intervals, stirring between intervals, until chips are completely melted. Set aside and allow to cool slightly (about 10 minutes, stirring occasionally).⅓ cup (57 g) dark chocolate chips

Cream room temperature butter with an electric mixer. Stir in slightly cooled chocolate and beat well.½ cup (1 stick) (113 g) butter

Gradually add sugar, scraping down the sides and bottom of bowl occasionally.1 ½ cup powdered sugar

Sprinkle in espresso powder, salt and vanilla extract, stir well.2 teaspoons espresso powder, ¼ teaspoon vanilla, ⅛ teaspoon salt

Gradually add heavy cream, increase speed to high and beat for 1 minute.1 Tablespoon heavy cream

Spoon into a piping bag (or a Ziploc bag with a corner snipped off)

Pair off your cooled chocolate cookies so each cookie has a mate.  Pipe a circle of vanilla frosting on the bottom of one cookie, fill the circle with piped chocolate espresso frosting.   Top with another cookie and serve!