Start by melteing or browning the butter. To brown the butter, first melt the butter in a skillet over medium heat. Stir occasionally at first. Once begins to bubble, 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.
Toast the pecans in a single layer in a dry skillet over medium heat. When you can smell the pecans toasting, toss them by shaking the skillet. Toss and shake a few times to be sure they toast evenly. It should only take about 5 minutes to toast them. Nuts can burn easily, so make sure not to leave the nuts on the stove. Transfer them to a plate or paper towel to cool. Once cooled, roughly chop the pecans.
In a medium sized bowl, whisk to combine the flour, baking soda, cinnamon and salt. Set aside.
In a large bowl, stir to combine the room temperature brown butter and sugars.
Add the egg followed by the egg yolk and the vanilla.
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 medium cookie scoop (or form cookies using about 2 tablespoons of cookie dough) to drop cookies on baking sheet. Place them 2 inches apart. Stick a couple of extra chocolate chips or toasted pecans on top of the cookie, if desired.
Bake 9-11 minutes until edges are lightly golden. Remove from oven. Cool for 5 minutes on the baking sheet. Transfer to a cooling rack to cool completely.