Preheat the oven to 325 degrees F (165 degrees C).

Cream butter, oil, white sugar, and confectioners' sugar together in a large bowl using an electric mixer until smooth. Beat in eggs, 1 at a time. Stir in vanilla extract.

Combine flour, baking soda, cream of tartar, and salt in a separate bowl. Stir gradually into the butter mixture. Stir in pecans.

Roll dough into 1-inch balls and place onto ungreased cookie sheets, about 2 inches apart.

Bake in the preheated oven until edges are golden, 12 to 14 minutes.

Remove from cookie sheets and cool completely on wire racks, 20 to 30 minutes.