Preheat oven to 375 degrees. Spray a 9 x 13-inch pan with nonstick baking spray.
Beat the butter and sugars until creamy. Add the egg, eggnog, and vanilla extract and beat until combined.
Combine the flour, baking powder, salt, and nutmeg. Slowly add it to the butter mixture until everything is mixed in.
Press it into the prepared pan. Bake for 15 minutes. Do not over bake. Let cool completely.
Beat the butter until creamy. Add the vanilla extract, eggnog, and salt and beat again.
Slowly add the powdered sugar until everything is creamy. Spread evenly over the cooled bars. Top with sprinkles. Gently press sprinkles into the frosting.