In a mixing bowl, using an electric mixer, cream the sugars, butter, oil, eggs and vanilla.  Add the flour, salt, baking soda and cream of tartar; mix well. Divide the dough into 4 cylinder shapes, each about 1 1/4 inches in diameter. Wrap in plastic wrap and chill until firm, about 2 hours. Preheat oven to 350ºF. degrees. Combine all the topping ingredients and set aside. Slice the chilled dough about 1/4 inch thick and place the slices on un-greased baking sheets about 1 1/2 inches apart. Using the back of a teaspoon, make a small depression in the center of each cookie and fill with about 1 teaspoon of the cherry topping. Bake for 8-10 minutes or until golden. Cool on the baking sheets, then remove the cookies, using a spatula.