Add butter to skillet over medium heat. Once butter has melted, whisk constantly. The butter will bubble and foam up slightly and then subside. This is when the browning will occur.
Watch for little brown flecks in the bottom of the pan. It should also smell nutty. Watch carefully as the butter browns, because it can burn quickly. Once the foamy has subsided and you see lots of little brown flecks, the butter has been browned.
Remove from heat and transfer to a bowl to stop the cooking process. Allow butter to come to room temperature. It doesn't need to be solid.
For the cookies
Line two baking sheets with parchment and set aside.
Preheat oven to 350°F
In a food processor (or plastic bag, smash with a rolling pin) pulse 2 cups of the Cap'n Crunch cereal until finely ground. Set aside in a bowl.
In the bowl of a stand mixer, fitted with the paddle attachment, beat together browned butter, brown sugar and granulated sugar until fluffy and pale in color.
Beat in vanilla, whole egg and egg yolk and continue beating until light and fluffy.
In a separate bowl, whisk together baking soda, salt, flour and finely ground Cap'n Crunch cereal.
Reduce mixer speed to low and beat in the flour mixture until just combined.
For rolling the cookies:
In a food processor (or plastic bag, smash with a rolling pin) pulse remaining 1 cup of Cap'n Crunch cereal until finely ground.
Portion dough into 2-3 Tbsp sized balls, then roll the cookie dough in the ground cereal and coat evenly. You can also add coarse pieces of cereal to the tops of each cookie, too.
Bake for 8-9 minutes. Aim to have them slightly under baked if you want them to still be slightly soft once baked.
Cool for 2-3 minutes on the baking sheet, then transfer to a rack to completely cool.