In a medium bowl, whisk together flour, baking soda, baking powder, salt, ground cinnamon and ground ginger.
In the bowl of a stand mixer (or with a hand mixer) cream together butter, brown sugar and granulated sugar. Beat in vanilla extract, one whole egg and one egg yolk.
Add the flour mixture to the wet ingredients and mix on low until just combined.
Use the small holes on a box grater to finely shred carrots. Add grated carrots and oats to the bowl and mix until just combined. Stir in white chocolate chips and walnuts.
Use a cookie scoop to measure out two tablespoon balls of cookie dough. Place dough balls on a parchment lined sheet pan, cover and chill in the refrigerator for at least two hours.
Preheat the oven to 350 degrees f. Place cookie dough balls at least two inches apart on a parchment-lined baking sheet.
Bake for 12-15 minutes, rotating cookie sheet halfway through, until edges are lightly golden brown and tops are no longer shiny. Cool on the baking sheet for 2-3 minutes before transferring to a wire rack to cool completely.
Notes
Store completely cooled cookies in an airtight container on the counter for up to five days. Baked cookies can be frozen for up to three months.