Position oven racks to upper and lower thirds and preheat oven to 350°F (180°C). Line baking sheets with parchment paper and set aside.
In a large bowl using a stand mixer fitted with the paddle or a hand mixer, beat the softened butter and dark brown sugar on medium speed until light and fluffy, about 2–3 minutes.
Add the instant pudding mix to the creamed butter-sugar and mix briefly so it’s evenly distributed. Beat in the eggs one at a time, then stir in the vanilla and espresso powder until smooth.
In a separate bowl whisk together the flour, unsweetened cocoa, baking soda, and salt to fully combine and remove any lumps.
With the mixer on low, add the dry ingredients to the wet mixture in two additions, scraping the bowl between additions. Beat just until no streaks of flour remain—do not overmix.
Fold in the dark chocolate chips with a rubber spatula until they are evenly distributed through the dough.
For chewier cookies and cleaner shaping, chill the dough in the refrigerator for 15 minutes. This short rest firms the dough so the cookies spread less in the oven.
Use a level tablespoon or small cookie scoop to portion dough (about 15 g each). Place balls 2 inches apart on prepared baking sheets. If desired, press a few extra chocolate chips into the tops for a pretty finish.
Bake one sheet at a time on the middle rack for 9–11 minutes, switching the pan front-to-back halfway through baking. Cookies should look set at the edges but still soft in the centers.
Remove the pan from the oven and let the cookies cool on the sheet for 3–5 minutes so they firm up, then transfer to a wire rack to cool completely.