Mix butter, shortening, eggs, and sugar until fluffy. With the mixer on low speed, add the flour to the butter mixture a little at a time. Mix well in between each addition.
Add vanilla and vinegar. Mix well. Add pecans and mix until nuts are evenly combined throughout.
Turn the dough out onto a lightly floured cutting board. Form the dough into a disk, then divide dough into four parts.
Shape each part into a seven-inch log. If baking immediately, allow dough to chill in the refrigerator for 1 hour before baking. Otherwise, wrap each cookie log in a layer of plastic wrap, then aluminum foil, and place them in the freezer.
Preheat oven to 300 degrees. Allow frozen cookie dough to sit at room temperature for 15 minutes before slicing.
Slice cookies about ¼-inch thick. Place on a greased cookie sheet. Bake for 8-10 minutes or until edges start to brown. Allow cookies to sit for five minutes before transferring to a cooling rack.
Notes
Each cookie log makes approximately 16-18 cookies. Make sure the baked cookies are completely cooled before transferring them to an airtight container. They can be stored at room temperature for up to a week. The frozen dough can be stored in the freezer for up to six months.