Preheat oven to 350 degrees. Line baking sheets with parchment paper.

In a large bowl with an electric mixer, beat butter on high speed for 2-3 minutes until fluffy. Add vegetable oil, 1 1/2 cups sugar, powdered sugar, eggnog, eggs and vanilla and mix well.

In a medium bowl whisk together flour, baking soda, cream of tartar, nutmeg, and salt. Gradually add dry ingredients to wet ingredients and mix until dough comes together.

Roll about 1/4 cup dough into a ball. Place remaining cup sugar in a small bowl. Roll the dough ball in the sugar to coat. Place on prepared baking sheet. Use the bottom of a tall glass or cup to flatten the cookie to about 1/2 inch thickness. The sides of the dough should squish out around the bottom of the glass to form an edge. Repeat with remaining dough, placing 6-8 cookies per baking sheet.

Bake cookies for 9-11 minutes or until cookies are set, but still pale. Do not over bake. Cool for 3-5 minutes on the baking sheet before removing to wire racks to cool completely.

Meanwhile, make the frosting by creaming butter and cream cheese with an electric mixer until fluffy. Mix in nutmeg, salt and vanilla. Add powdered sugar and mix until very thick. Add eggnog one tablespoon at a time until frosting reaches desired consistency . Spread on cooled cookies.