Preheat oven to 350 and place rack to middle position. Line a sheet pan with parchment paper.
Pour pecans into food processor and chop into small pieces. Add the next 6 ingredients and pulse to mix.
Cut butter into small pieces and add to food processor, processing until incorporated. It will not come together as a dough.
In a small bowl, beat the vanilla into the egg white. Pour mixture evenly around the ingredients in food processor and process until dough is evenly moist. It may or may not form a ball of dough but should hold together if squeezed lightly in the hand. If not, add 2 tsp water and process again.
Cover and refrigerate dough for 1 hour.
Scoop dough, pushing it firmly into the scoop on the inner side of the bowl. Place cookie dough on parchment lined baking sheet 2 inches apart. Dip tops into sweetener to prevent sticking while flattening. Using a piece of waxed paper and a flat bottomed glass or measuring cup, flatten the cookies - they will not spread.
Bake 10-15 minutes or until cookies begin to brown around the edges. Let sit for 5 minutes before transferring to a cooling rack. Do not eat the cookies until completely cool, about 2-4 hours.
Makes 18 cookies with each cookie having 0.80 g NET CARBS PER COOKIE.
Store the cookies in an airtight container on the counter for a week, in the refrigerator for several weeks or in the freezer for several months. I have not tried baking from frozen, but consider freezing cookie portions and thawing what you need in the refrigerator before shaping and baking.