Place the butter in a light-colored medium saucepan and melt over medium heat, stirring often, until it foams, smells nutty, and browns. This will take about 5 to 7 minutes. Scrape the browned butter into a large bowl. Let cool to room temperature. You can put it in the fridge to speed up the process.
In a medium bowl, whisk together the flour, baking soda, and salt.
In the bowl of a stand mixer, combine the browned butter, brown sugar, and granulated sugar. With the beater blade, mix until well combined. Add the egg, egg yolks, and vanilla. Mix until smooth, scraping down the sides of the bowl with a spatula as necessary.
Turn off the mixer and add all the dry ingredients. Mix on low until just combined. Don’t over mix.
Stir in the chocolate chunks (can use chocolate chips). Wrap the dough in plastic wrap and chill the dough for 2 hours. You can chill for up to 48 hours. If you want, you can go ahead and scoop the cookies into balls and chill the balls in an airtight container.
When ready to bake, remove the dough from the fridge and preheat the oven to 350 degrees F. If you haven't formed the balls, scoop the dough into balls, about 2 tablespoons per cookie, and place on a large baking sheet that has been lined with parchment paper or a Silpat baking mat. Leave about 2-inches of space between each cookie.
Bake for 10 to 14 minutes or until cookies are set around the edges, but still soft in the center. Remove from the oven and sprinkle with flaky sea salt. Let the cookies cool on the baking sheet for 5 minutes. Transfer to a cooling rack and cool completely.