Preheat oven to 325° F (165° C). Line two rimmed baking sheets with parchment paper and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, light brown sugar, and granulated sugar until light and fluffy, about 5 minutes.
Add the eggs one at a time, mixing until well combined after each addition. Scrape down the sides of the bowl as needed.
Mix in the orange extract and orange zest for about 30 seconds.
Add the flour, baking soda, baking powder, and salt. Mix until just combined.
Stir in the chopped dark and milk chocolate until evenly distributed throughout the dough.
Scoop the dough into 2 ½ tablespoon portions and place them about 2 inches apart on the prepared baking sheets. Bake for 13–15 minutes, until the edges are set and the centers are still slightly soft.
Sprinkle with flaky sea salt immediately after baking, if desired. Let the cookies cool on the baking sheet for 5–10 minutes, then transfer them to a wire rack to finish cooling.