Start by browning the butter. Melt the butter in a skillet over medium heat. Stir occasionally at first. Once begins to bubble and comes to a boil, stir it constantly. It will start to foam. Continue stirring as you watch for it to turn a light, amber color and develop a nutty smell which should happen in about five minutes. Pour the brown butter into a heat safe bowl, making sure the scrape the bottom of the pan for all the bits. Set the butter aside and use when cool to the touch.
In a medium sized bowl, whisk to combine the all purpose flour, oats, baking soda, and salt. Set aside.
In a large bowl, stir to combine the brown butter and sugars.
Stir in the vanilla extract followed by the egg and egg yolk and maple syrup.
Stir in the dry ingredients in two additions. Stir until just combined.
Stir in the chocolate chips and chopped nuts. Do not overmix.
Cover the bowl with plastic wrap. Chill 30 minutes.
When ready to bake, preheat oven to 350 F. Line baking sheets with parchment paper. Use a 2 tablespoon cookie scoop to drop cookies on baking sheet. Place them 2 inches apart.
Bake 10-12 minutes until edges are golden and middles have puffed up. Remove from oven. Cool for 10 minutes on the baking sheet. Transfer to a cooling rack to cool completely.