In a medium saucepan, melt the butter over medium heat until melted. Remove from the heat. Add the dark brown sugar and granulated sugar and stir until sugars are incorporated and smooth.
Chill this mixture for 10 minutes.
Remove from the refrigerator and stir in the egg, egg yolk and vanilla.
Add the flour, oats, baking soda, salt and cinnamon and mix together.
Stir in the white chocolate chips and the chocolate chips.
Roll by hand into 24 medium size balls or use a scoop, and place on a light-colored cookie sheet.
Chill for at least 30 minutes.
Preheat the oven to 325º F.
Remove the cookies from the refrigerator and bake for 12-14 minutes.