Prepare dry ingredients: In a medium bowl whisk together flour, baking soda, and salt until combined. Set aside.
Brown the butter: Add unsalted butter to a saucepan over medium heat. Let it melt, then bubble and foam — stir occasionally. When the foam subsides and golden brown specks form on the bottom and it smells nutty and caramel-like, remove from heat immediately to prevent burning. Allow the butter to cool to room temperature before using.
Combine wet ingredients: Pour the cooled brown butter into a mixing bowl. Add heavy cream, granulated sugar, and dark brown sugar. Whisk until smooth. Add egg, egg yolk, and vanilla extract and whisk until fully combined.
Add dry ingredients: Add the flour mixture to the wet ingredients and fold until you still see a few streaks of flour remaining — don't overmix.
Add chocolate: Fold in the chopped chocolate until evenly distributed and no dry flour remains.
Chill the dough: Cover and refrigerate the cookie dough overnight for the best flavor, texture, and structure. If baking same day, chill for at least 1 hour to stabilize the dough and prevent spreading. When I refrigerate overnight, the next day I will take it out and leave it at room temperature for around 30 min if I want thinner more rippled cookies.
Portion the dough: Use a cookie scoop to portion the dough into 8-9 large balls.
Bake: Preheat oven to 350°F (175°C). Place dough balls on a parchment-lined baking sheet with a good amount of space in between each cookie (they spread a good amount) and bake for 12-15 minutes or until the edges are set and the centers look slightly underdone — they will continue to set as they cool.
Cool and serve: Let the cookies cool on the baking sheet for at least 10 minutes before eating. Sprinkle with flaky sea salt if desired.