Melt the butter in a medium saucepan over medium heat. Add the carrots and simmer over medium low heat for 2-3 minutes, until the carrots soften. Remove from the heat and add the brown sugar. Stir well to combine thoroughly. Add the egg, orange zest and the vanilla and stir to combine.
Whisk the remaining dry ingredients together and then add to the mixture in the pan. Stir to combine and then chill in the refrigerator for at least 1 hour. Preheat the oven to 325°F. Line a baking sheet with a silpat mat or parchment and then use a medium scoop to place large (2) tablespoon scoops on the tray. The cookies will spread considerably, 6 cookies should fit on a large baking sheet.
Bake for 12 minutes, until the edges are just barely browned. Let the cookies cool on the baking sheet for at least 8-10 minutes, before removing them to a cooling rack. Enjoy!