In a medium bowl, whisk together the flour, cream of tartar, and baking soda. Set aside.

Using an electric mixer, cream together the vegetable shortening, granulated sugar, and powdered sugar until light and fluffy. Add the vanilla extract, salt, and egg and beat until smooth and fully incorporated.

Gradually add the flour mixture to the wet ingredients, about one-third at a time, mixing until a thick dough forms. Fold in the chopped pecans.

Refrigerate the dough for 30 to 45 minutes.

Preheat the oven to 350°F. Line a baking sheet with parchment paper or leave it ungreased.

Roll the chilled dough into 1- to 1 1/4-inch balls and place them on a baking sheet. Flatten each ball to about 1/4 inch thick and smooth the edges.

Bake for 12 to 15 minutes, until the edges are just beginning to turn golden. Cool on the baking sheet for a few minutes before transferring to a wire rack.