Place the cubed butter in a medium saucepan over medium heat. Melt the butter completely, then continue to cook, stirring occasionally, until it turns a deep amber color and nutty brown bits form at the bottom. This should take about 5-8 minutes. Immediately pour the browned butter (including all the brown bits) into a large heatproof mixing bowl and let cool for 10-15 minutes until it's just warm to the touch.

Add the granulated sugar and brown sugar to the cooled brown butter. Using a stand mixer with the paddle attachment (or a hand mixer), beat on medium speed for 2-3 minutes until light and fluffy. Scrape down the sides of the bowl.

Add the egg, then the egg yolk, beating well after each addition until fully incorporated. Mix in the vanilla extract.

In a separate medium bowl, whisk together the flour, baking soda, and fine sea salt.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix; overmixing can lead to tough cookies.

Fold in both types of chocolate chips with a rubber spatula until evenly distributed.

Cover the bowl with plastic wrap and refrigerate the dough for at least 30 minutes, or up to 2 hours. Chilling helps prevent the cookies from spreading too much and deepens the flavors.

Preheat your oven to 375°F (190°C). Line two baking sheets with parchment paper.

Using a 2-3 ounce ice cream scoop, portion out the chilled dough onto the prepared baking sheets, leaving about 2-3 inches between each cookie.

Bake one sheet at a time for 10-14 minutes, or until the edges are golden brown but the centers still look slightly underbaked and gooey. The exact time will depend on your oven.

Immediately after removing from the oven, sprinkle the tops of the hot cookies with flaky sea salt.

Let the cookies cool on the baking sheet for 5-10 minutes before transferring them to a wire cooling rack to cool completely. This allows them to set and firm up.