Line an 8X8 metal baking pan with parchment paper. Preheat the oven to 350°F.
Brown the butter first. To brown butter, melt the unsalted butter in a saucepan over medium heat, stirring frequently. Once melted, it will foam and begin to turn golden, then brown. Keep stirring to prevent burning, and when it reaches a nutty aroma and deep brown color, remove it from the heat and let it cool.
Whisk together the flour and salt, set aside.
Place the dark brown sugar and granulated sugar in a bowl, add the cooled down brown butter, scrape the bits of the brown butter off of the bottom of the pan. Mix until combined.
Add the egg, egg yolk, and vanilla, mix until combined.
Add the flour and salt, mix until just combined. Mix in the chocolate chips.
Pour into the baking pan, spreading it out evenly. Sprinkle the Christmas sprinkles evenly over the top.
Position it on the center rack of the oven to ensure even baking, avoiding placement too close to the top or bottom. Bake for 22-25 minutes, the top will look just set and the center will be slightly wobbly. Do not over bake, check at 22 minutes.
Sprinkle with flaky sea salt. Let cool before cutting. See storage below in notes.