Line a large plate or baking sheet with parchment paper.

Brown the butter: Melt the butter in a small saucepan over medium heat. Once melted, whisk constantly; the butter will begin to crackle, then foam. After a few minutes, the butter will begin to turn a golden amber color. As soon as the butter turns brown and gives off a nutty aroma, 5 to 8 minutes, remove from the heat and immediately transfer it to a medium bowl, scraping all the butter and brown bits from the pan. Set aside until cool enough to touch, about 15 minutes.

Mix the wet ingredients: In the bowl of a stand mixer fitted with the paddle attachment, mix the brown butter, brown sugar, and granulated sugar until well combined, about 1 minute. Beat in the egg, egg yolk, vanilla, and yogurt until the mixture is smooth and creamy and similar in appearance to a caramel sauce, about 1 minute.

Prepare the dry ingredients: In another large bowl, whisk the flour, baking soda, and salt until well combined. With the mixer running on low speed, slowly add the dry ingredients to the wet ingredients and mix just until combined, about 1 minute. Add both types of chocolate chips and mix on low speed until just incorporated into the dough (don’t overmix!). Cover the bowl with plastic wrap and place in the fridge for 10 minutes.

Chill the dough: Use a medium cookie scoop or spoon to measure 2 heaping tablespoons of the dough, roll the dough into balls with your hands, and place onto the prepared plate or baking sheet. Repeat with all of the dough. Cover the balls with plastic wrap and refrigerate for a minimum of 2 hours and a maximum of 24 hours.

When you are ready to bake, place a rack in the middle of the oven and preheat to 350°F. Line a large baking sheet with parchment paper. Remove the dough from the fridge to allow them to soften for 15 minutes.

Bake the cookies: Transfer the dough balls to the prepared baking sheet, placing them 2 inches apart. Bake until the edges of the cookies just begin to turn golden brown, 9 to 11 minutes.

Cool the cookies on the sheet for 5 minutes to allow them to set, then sprinkle each cookie with flaky sea salt. Transfer to a wire rack to cool completely. Once the baking sheet has cooled, repeat with the remaining dough balls.

To store: Keep cookies in an airtight container or reusable silicone bag at room temperature for up to 1 week, then transfer to the freezer for up to 3 months.