Heat the oven to 375°F. Line two baking sheets with parchment paper and set aside.
Whisk the flour, cocoa, baking powder, salt, and espresso powder in a medium bowl to combine. Set aside.
Place the butter and chopped bittersweet chocolate in a large microwave-safe bowl. Microwave at 50% power in 30-second bursts, stirring between each, until smooth and fully melted, 1 1/2 to 2 minutes total. (Alternatively, melt over a saucepan of gently simmering water.)
While the chocolate mixture is still warm, whisk in the granulated and brown sugars until glossy. Let sit 2 minutes to cool slightly.
Whisk in the eggs one at a time until the batter looks thick and shiny, then whisk in the vanilla.
Switch to a spatula and fold the dry ingredients into the chocolate mixture just until a few streaks remain. Fold in the chocolate chips until evenly distributed. The batter will be soft and shiny.
Let the batter rest at room temperature for 10 to 15 minutes to thicken slightly (or chill 10 minutes if your kitchen is warm).
Scoop 1 1/2-tablespoon portions of dough onto the prepared sheets, spacing about 2 1/2 inches apart.
Bake 7 to 9 minutes, rotating the pans halfway, until the tops are crackly and the edges are set but centers are still soft. If using, sprinkle a tiny pinch of flaky salt over the hot cookies.
Cool on the pans for 5 minutes, then transfer to a wire rack to cool completely. The cookies will firm as they cool.