In a stainless steel skillet or another light-bottomed pan over medium-high heat, melt the butter, swirling the pan occasionally. The butter will foam as the water boils off. Watch closely at this stage. Tiny brown specks of milk solids will appear at the bottom of the pan; constantly stir and scrape these off with a spatula to prevent sticking.
As soon as the butter turns chestnut brown and smells nutty, remove it from the heat and pour into a heat-safe bowl.
To the hot browned butter, add the light brown sugar and stir to combine. Let the mixture cool for 15-20 minutes.
In a medium bowl, whisk together the flour, baking soda, kosher salt, and baking powder.
Once the butter mixture has cooled, add the eggs and vanilla extract. Whisk until fully combined.
Using a rubber spatula, gradually mix the dry ingredients into the wet ingredients until just combined.
Fold in the chopped semi-sweet chocolate.
Using a 3-tablespoon scoop, portion out balls of dough and place them on a baking sheet lined with parchment paper. Cover the dough balls and chill in the refrigerator for 24 hours.
Remove the chilled cookie dough from the refrigerator and let it rest at room temperature for 30 minutes.
Preheat the oven to 350°F and line baking sheets with parchment paper.
Place the dough balls onto the lined baking sheets, leaving about an inch of space between each one. Bake for 12-14 minutes, or until golden brown. For slightly underdone cookies, begin checking at 10 minutes.
Remove the baking sheets from the oven and sprinkle the tops of the warm cookies with flaky sea salt.
Let the cookies cool on the baking sheets for 5 minutes, then transfer them to a wire rack to cool completely.