Preheat oven to 350° F / 175° C. Line 2 half-sheet rimmed baking trays with parchment or a silicone baking mat.

In a large bowl, whisk together all purpose flour, cocoa powder, granulated sugar, baking powder, instant espresso, and fine sea salt.

Add the cubed butter and use your hands to combine, rubbing together until the mixture resembles coarse breadcrumbs, with no large chunks of butter remaining. You should still see some strands or pea-sized pieces.

With a bench scraper, work in the eggs and vanilla extract.

With your hands, gently knead until a soft dough forms. Knead in the miniature chocolate chips.

On a lightly floured countertop, divide dough into two equal portions, then roll each portion into a log. Each log should measure approximately 7 inches long x 1 1/2 inches wide.

Arrange on 1 of the prepared trays, allowing 4-5 inches of space between the logs. With a pastry brush, brush the top of each log with beaten egg white.

Bake in preheated oven for 25 minutes. Remove from oven and reduce oven temperature to 325° F / 162° C.

Cool on tray for 10 minutes, then transfer logs to a chopping board. With a serrated knife, slice diagonally into 1/2- to 3/4-inch thick slices.

Arrange upright on prepared trays, allowing 2-3 inches of space in between the slices. Bake 20 minutes, or until dry to the touch.

Cool completely on a wire rack.

Sit wire rack over a large tray lined with a sheet of parchment or wax paper.

Melt chopped dark chocolate over a double boiler or bain marie, or in short increments in the microwave, stirring until completely melted. Scoop into a disposable piping bag.

Pipe zigzags of melted chocolate over biscotti, allowing the excess chocolate to drip onto the tray below.

Allow biscotti to sit at room temperature, uncovered, until chocolate sets. Serve immediately.

Layer leftover double chocolate biscotti in an airtight container between sheets of parchment or wax paper. Store at room temperature for up to 5 days, or freeze for up to 3 months.