Preheat your oven to 325°F. Position your racks in the top third and lower third of the oven. Line two baking sheets with parchment paper.
In a large mixing bowl, beat the dark brown sugar, butter, and granulated sugar on medium speed until light and fluffy. This should take about 3 minutes.
Add the egg and vanilla extract to the creamed mixture. Beat for another 30 seconds until everything is well combined.
In a separate bowl, whisk together the flour, espresso granules, baking powder, kosher salt, and baking soda. Gradually add this dry mixture to the butter mixture, beating on low speed until just combined.
Stir in 3/4 cup semi-sweet chocolate chips, 1/2 cup bittersweet chocolate chips, and 1/2 cup chopped milk chocolate.
Use a 1-ounce scoop or a 2-tablespoon measure to portion the dough onto prepared baking sheets, spacing each scoop about 2 inches apart.
Top each dough mound with the remaining 1/4 cup bittersweet chocolate chips and 1/2 cup chopped milk chocolate. Reserve the last cup of milk chocolate for later.
Bake the cookies for 7 minutes, then take them out and quickly dot the tops with the reserved milk chocolate. Rotate the baking sheets and bake for an additional 8 minutes until the edges are lightly golden brown.
Remove from the oven and immediately sprinkle with a pinch of flaky sea salt. Let the cookies cool on the pan for 5 minutes before transferring to a wire rack to fully cool.