In a 3-quart pot (or medium saucepan), add the butter. Put over low/medium heat and melt completely. Once melted, continue to stir the butter while it browns. This can take about 10 minutes; the butter will turn from a yellow color to a light golden brown color and small brown speckles (little brown bits) will appear. Remove from heat immediately when you see this happening, as it can easily burn.
In the bowl of a stand mixer fitted with the paddle attachment, add the brown butter, cane sugar, eggs, and vanilla extract. Mix on low until combined.
Add the flour, baking powder, and sea salt and mix on low until combined.
Add the chopped chocolate bars into the dough and mix to combine completely.
Line 1 baking sheet with parchment paper.
Using your hands (or a cookie scoop) ball the dough into 12 balls and place onto the prepared baking sheets. Refrigerate dough balls for at least 1 hour.
Preheat the oven to 375°F. Line another baking sheet with parchment paper and transfer half the cookie dough to the second baking sheet. Spread out the cookies so they are evenly spaced apart on each sheet (2x3).
Bake for 15 to 17 minutes or until they are golden brown around the edges. Sprinkle with flaky sea salt immediately after coming out of the oven.
Store in an airtight container for up to 7 days.