Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking pan.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the egg, vanilla extract, and eggnog yogurt until well combined.
Gradually add the all-purpose flour, baking powder, and baking soda to the mixture, mixing until just combined.
Press the cookie dough evenly into the prepared baking pan.
Bake in the preheated oven for about 20-25 minutes, or until the edges are lightly golden. The center might still be slightly soft, but it will set as it cools.
Allow the bars to cool completely in the pan on a wire rack.
For the frosting, whisk together powdered sugar, 1/4 cup eggnog milk, vanilla extract, and a pinch of nutmeg until smooth and creamy.
Once the bars are cooled, spread the frosting evenly over the top.
Optionally, sprinkle a bit of extra nutmeg on top of the frosting for extra flavor.
Allow the frosting to set before cutting the bars into squares.