For the cookies: Line 3 baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking soda, cinnamon, baking powder, ginger, salt, and nutmeg. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, brown sugar, and granulated sugar on medium speed until light and fluffy, 3 to 5 minutes. Scrape down the sides of the bowl and beat in the vanilla and egg. Reduce the speed to low and slowly add the flour mixture, mixing until combined, about 1 minute. Remove the bowl from the mixer and carefully stir in the green cherries, red cherries, pecans, walnuts, and orange peel.
Using a 2 tablespoon-cookie scoop, scoop the dough onto the prepared baking sheets, spacing the dough balls about 3 inches apart. Chill the dough for at least 30 minutes and up to overnight.
Preheat the oven to 375°F.
Working in batches if necessary, bake the cookies, rotating the pans halfway through, until lightly golden around the edges, 12 to 14 minutes. Transfer the cookies to a cooling rack and allow them to cool completely.