In a medium bowl, sift together the flours, salt, and baking soda. Set aside.
In a medium or large saucepan, add the butter and melt over medium heat. The larger the pan you use, the quicker the process will be!
Bring the butter to a boil, stirring frequently. As the water begins to boil out of the butter, the milk solids in the butter will separate, sink to the bottom, and begin to toast and brown. As this begins to happen, make sure to stir constantly so the butter browns evenly. It may become quite foamy, splatter a bit, and be difficult to see, so keep a close eye on it, removing from heat and continuing to stir if it starts to foam over.
Once the butter has turned a nice nutty brown, remove from the heat and pour into a large liquid measuring cup to stop the cooking. Allow it to cool down for a minute or two, give it a stir, and carefully add 2-3 tablespoons of water to the butter to bring it back up to 1 cup (240 ml) of liquid.
Set aside to cool to room temperature. To help speed this process up, you can place in the fridge for 10-15 minutes. You want to make sure the butter is still liquid when you’re adding it to the dough later on, so make sure to remove after 15 minutes.
In a large bowl, add the sugars, vanilla, espresso powder, and cooled brown butter. Cream together with an electric hand mixer until light and fluffy, 1-2 minutes.
Add the egg and yolk and beat until incorporated.
Add the dry ingredients, about ⅓ of the mixture at a time, and beat between additions until just incorporated. It’s okay for there to be a bit of unmixed flour on the edge of bowl, this will be incorporated in the next step.
Using a wooden spoon, fold the chocolate chips and chunks into the dough.
Scoop the cookies onto a parchment paper-lined baking sheet in 3-tablespoon-sized mounds.
For optimal flavor, cover and refrigerate for 1 hour or, even better, overnight.
Preheat the oven to 350˚F (180˚C).
Evenly space the dough 3 inches (8 cm) apart from one another on a parchment paper-lined baking sheet.
Bake in a preheated oven for 12-14 minutes.
Let the cookies cool on the baking sheet for 2-3 minutes before transferring to a cooling rack to cool completely.