Step 1: In a light-colored saucepan, melt the unsalted butter over medium heat. Cook, stirring constantly, until the butter turns a rich amber color and smells nutty. This usually takes 5-8 minutes. Immediately pour the brown butter, including all the browned milk solids, into a heatproof bowl. Let it cool for 15-20 minutes, or until slightly warm.
Step 2: In a large mixing bowl, combine the cooled brown butter with both brown sugar and granulated sugar. Beat with an electric mixer on medium speed until light and fluffy, about 2-3 minutes.
Step 3: Add the egg and egg yolk, one at a time, beating well after each addition. Stir in the vanilla extract.
Step 4: In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Step 5: Fold in the chocolate chips and chunks until evenly distributed throughout the dough.
Step 6: Cover the bowl with plastic wrap and refrigerate the dough for at least 30 minutes, or up to 2 hours for best results. This helps the flavors meld and prevents excessive spreading.
Step 7: Preheat your oven to 375°F (190°C). Line baking sheets with parchment paper or silicone baking mats.
Step 8: Scoop rounded tablespoons of cookie dough onto the prepared baking sheets, leaving about 2 inches between each cookie.
Step 9: Bake for 10-12 minutes, or until the edges are golden brown and the centers are still slightly soft. They will continue to set as they cool.
Step 10: Remove the baking sheets from the oven and let the cookies cool on the sheets for 5 minutes before transferring them to a wire rack to cool completely.