Cube the butter and place in a light-colored skillet. (Light-colored helps you determine when the butter begins browning.) Melt the butter over medium heat, stirring constantly.
Once melted, add the milk powder and stir until evenly incorporated (don't worry if some of the milk powder clumps together). Keep stirring. After 5-8 minutes, the butter will begin browning; you’ll notice lightly browned specks begin to form at the bottom of the pan, and you'll begin to smell a nutty aroma. Once browned, immediately remove from heat and pour into a heat-proof bowl.
To the brown butter (which should look like dark, wet sand), add the brown sugar and granulated sugar and whisk until evenly combined. Add the egg and vanilla and whisk again until well combined.
Add the flour, baking soda, and salt to the wet ingredients and mix until just combined; be sure not to overmix! Fold in most of the chocolate chunks (reserve some for the next step) until incorporated.
Using a 3-tablespoon spring-loaded scoop, scoop the dough into balls and place dough balls on a lined baking sheet. Top with remaining chocolate chunks, then place in the refrigerator to chill for 30 minutes.
Preheat the oven to 350°F (180°C). Line another baking sheet with parchment paper and set aside.
Bake the cookies, 4 at a time, for 10-12 minutes, or until browned on the sides; the centers will look soft. Remove from the oven and sprinkle the tops with flaky salt. Allow to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.