Mix together flour, baking soda, and cream of tartar and set aside.
In the bowl of a stand mixer, or another large bowl (if using a hand mixer), cream butter, and sugars together until fluffy. Then add vanilla, salt, and egg and beat until smooth.
Slowly add the flour mixture to the sugar mixture and mix well after every addition, the dough will be a little thick.
With a large spoon, add the pecans and mix.
Cover the bowl with plastic wrap and chill for 30-45 minutes.
Pre-heat oven to 350 degrees.
Roll dough out in 1 1/2 - 2 inch balls and put on to an un-greased baking sheet.
Bake for 15-18 minutes until cookies are slightly browned (this will depend on the size of your cookies, if cookies are larger they can take up to 20 minutes)
Cool on a wire rack and enjoy! Store in a air tight container.