Preheat oven to 375 degrees. In a large bowl, cream together the butter, vegetable oil, 1 cup white sugar, and powdered sugar until smooth.
Beat in the eggs one at a time, then stir in the vanilla. Combine the flour, baking soda, cream of tartar and salt; stir into the creamed mixture. Roll dough into 1 inch balls and roll each ball in remaining white sugar. Place the cookies 2 inches apart onto ungreased cookie sheets and place pecan halve on top. Press lightly.
Bake cookies for 10 to 12 minutes in the preheated oven, or until the edges are golden. Remove from cookie sheets to cool on wire racks. Makes 8 dozen cookies. Enjoy!
Optional: If desired you may stir chopped pecans into dough before baking, instead putting of halves on top of each cookie.