Wash the cranberries thoroughly and discard any soft or damaged berries. Using a microplane or fine grater, zest the entire orange into a large bowl. Cut away the remaining white pith from the orange and roughly chop the flesh. Core the apple and cut into quarters (no need to peel if using organic).
Working in batches if necessary, pulse the cranberries, orange segments, and apple pieces in a food processor until finely chopped but not pureed. You want a consistent texture with small, identifiable bits of fruit – about 8-10 pulses should do it.
Transfer the chopped fruit mixture to a large bowl. Add both sugars, cinnamon, and nutmeg. Gently fold everything together until well combined. The sugar will begin to draw out the juices from the fruit.
Stir in the orange liqueur (if using) and optional nuts. Cover the bowl and refrigerate for at least 2 hours, but preferably overnight. This resting time allows the flavors to meld beautifully and the sugar to fully dissolve.
Taste the relish before serving and adjust sweetness if needed. Serve chilled as a side to your holiday meal.