In a medium bowl, whisk together the flour, cocoa powder, cornstarch, baking soda, salt, and espresso powder until evenly combined (sift the cocoa if lumpy).
In a stand mixer fitted with the paddle (or using a hand mixer), beat the softened butter and brown sugar on medium speed until creamy and slightly lightened, about 2 minutes. Add the granulated sugar and beat 1 minute more, scraping the bowl as needed.
Mix in the vanilla, then the egg, and finally the yolk, beating just until smooth after each addition.
Add the dry ingredients in two additions on low speed until no dry streaks remain. The dough will be soft. Cover and chill the bowl for 15–20 minutes to firm slightly for easier scooping.
While the dough chills, heat the oven to 360°F (182°C) and line two baking sheets with parchment paper.
Scoop the dough into 1 1/2-tablespoon portions (about 24 balls). Roll each in the sanding or granulated sugar to coat, then set on the prepared sheets 2 inches apart. Lightly press each ball with the bottom of a flat glass to about 1/2-inch thick.
Bake 9–11 minutes, rotating the pans halfway through. For extra crackly tops, rap the baking sheet once on the oven rack at the 8-minute mark, then finish baking until the edges look set but centers are soft.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack. Tip: For perfectly round, neat edges, gently scoot a round cookie cutter around each warm cookie before moving it to the rack.
Repeat with remaining dough. If the dough softens as you work, return it to the fridge for 5 minutes between batches.