First, brown your butter: add butter to a large saucepan and place over medium heat. The butter will begin to crackle, and then eventually foam. Make sure you whisk constantly during this process. After a couple of minutes, the butter will begin to brown and turn a nice golden amber color on the bottom of the saucepan. Continue to whisk and remove from heat as soon as the butter begins to brown and give off a nutty aroma. Immediately transfer the butter to a medium bowl to prevent burning. Set aside to cool for 10 minutes or until cool enough to touch.
Once brown butter has cooled down a bit, add all (including the brown bits) of it to the bowl of an electric mixer, along with the dark brown sugar, granulated sugar and lime zest. Mix on medium speed for about 1-2 minutes
Next, add in the egg, egg yolk and vanilla and beat on medium speed until well combined, smooth and creamy; about 1-2 minutes.
In a separate bowl, whisk together the flour, baking soda and salt in a bowl. Slowly add the dry ingredients to the bowl of the electric mixer and beat on medium-low speed just until combined. Next add in the white chocolate chunks chopped macadamia nuts, and graham crackers, if using. Mix on low speed until just combined.
Use a cookie scoop to grab about 2 tablespoons of dough and roll into balls. Place on a plate or platter, cover with plastic wrap and chill in the fridge for 1 hour or up to overnight. If you are super eager, place it in the freezer for 15-20 minutes.
Once ready to bake, preheat the oven to 350 degrees F. Let your dough balls sit at room temp for 15-20 minutes while your oven preheats so they are not overly cold when you go to bake them.
Place dough balls on baking sheet, 2 inches apart. Bake the cookies 9-11 minutes or until the edges of the cookies begin to turn golden brown. They will look a bit underdone in the middle, but will continue to cook once out of the oven. Bake longer if you like crispier cookies, but I do not recommend.
Cool the cookies on the sheets for at least 5 minutes. Remove the cooled cookies from the baking sheets after a few minutes and transfer to a wire rack to cool completely. Repeat with remaining dough. Makes about 20 cookies.