In a bowl, whisk the flour, baking powder, salt and walnuts until well combined; set aside.
Using a stand mixer fitted with the paddle attachment, cream the eggs and sugar until light and fluffy.
With the mixer on medium speed, add the oil in a slow, steady stream.
Add the vanilla extract and mix to combine.
Scrape down the sides of the bowl and mix once more to ensure a homogenous mixture is reached.
Add the dry ingredients and mix just long enough to combine.
Form two logs measuring 2 ½” by 10 ½” on a parchment-lined baking sheet.
Sprinkle one log with red sanding sugar and the other with green.
Bake until the edges are golden, for 20 to 25 minutes.
Cool for 5 minutes before transferring to a cutting board.
Using a serrated knife, cut the logs into ¾” cookies.
Cool completely on a cooling rack before storing in an airtight container for up to 2 weeks.
Notes
To shape the logs with ease, run your hands under cold water, give a shake and form the logs. The water will keep the oily batter from sticking to your hands.