In a large bowl, with a mixer on medium speed, beat 1/2 cup butter, granulated sugar, and powdered sugar until smooth. Add oil, egg, and vanilla and beat until well blended.
In a medium bowl, mix 2 cups flour, baking soda, nutmeg, and salt. Stir into butter mixture, then beat until well blended. Cover bowl with plastic wrap and freeze until dough is firm, about 1 hour.
Shape dough into 1-inch balls and place about 2 inches apart on buttered 12- by 15-inch baking sheets. Press each cookie with the lightly floured tines of a fork to flatten slightly.
Bake cookies in a 350° regular or convection oven until edges are lightly browned, 8 to 10 minutes; if baking two sheets at once in one oven, switch their positions halfway through baking. Let cookies cool on sheets for 5 minutes, then use a wide spatula to transfer to racks to cool completely.
Nutritional analysis per cookie.