In a large saucepan over medium heat, add the butter. Whisk the butter as it melts and continue to heat the butter as it starts to brown. The color will change from bright golden yellow to a darker amber. Once the butter turns color, remove it from the heat and allow it to cool for about 10 minutes.
While the brown butter is cooling, in a separate large bowl, whisk together the flour, baking soda and salt. Set aside.
Once the butter is cool to the touch, add it to a large stand mixer, and beat together with the light brown sugar and granulated sugar until combined. Then beat in the egg, egg yolk, vanilla, sour cream, and instant espresso until combined.
Gradually add in the dry flour mixture into the wet mixture just until combined. Then use a silicone spatula to gently fold in the chocolate chips and espresso chips.
Shape the dough into a round flat disc shape, wrap in plastic wrap or parchment or wax paper, and refrigerate for at least two hours.
Once the dough has been refrigerated for at least two hours, preheat the oven to 350°F. Line two baking sheets with parchment paper.
Remove from the refrigerator and use a medium scoop to scoop out the dough and form the dough into balls. Place them about 2 inches apart on the prepared baking sheets to give them room to spread while baking.
Bake at 350°F for 9 to 11 minutes, just until the edges are slightly browned but the centers are still slightly soft.
Remove from the oven and allow to cool on the baking sheets for 5 minutes, then transfer them to a cooling rack until they have cooled completely.
Notes
Chilling the dough: It's a good idea to chill your dough for a couple of hours before you bake the cookies so the fat can solidify. This helps keep the cookies from spreading too thin when baked, resulting in a thicker, fuller cookie.