Preheat oven to 350 degrees Fahrenheit. Line 2 baking sheets with parchment paper and set aside.
In the bowl of a stand mixer, beat the butter and sugars until light and fluffy (this may take a few minutes).
Scrape the sides of the bowl, then add the egg and vanilla extract, mixing until well-blended.
On low speed, add the baking soda, salt, gradually adding the flour as it mixes. Mix until just incorporated.
Remove bowl from mixer and stir in the chips and nuts until well-distributed.
Using a small cookie scoop, portion out dough on prepared baking sheets. Bake, one sheet at a time, until edges are lightly browned, or about 9 minutes.
Cool for 2 minutes on baking sheet before removing to wire racks to cool completely.
Cookies can be stored in an air-tight container for up to 4 days at room temperature.