Slice cabbage in half lengthwise, so that stem keeps each half together. Shred each half into ¼” to 1/2" ribbons using a v-slicer, mandoline, cabbage shredder or good ol' chef’s knife.
Add salt to shredded cabbage.
Rinse orange to remove dirt. Zest it with a microplane or fine grater, being careful to only include the outer orange portion, not the pithy white portion (which tastes bitter). Add to cabbage.
Cut top off pepper. Separate seeds and membrane from flesh and discard. Finely dice flesh and add to cabbage.
Massage contents thoroughly for a few minutes with clean or gloved hands, or pound until brine forms.
Add cranberries, cracking about half of them. Gently mix until they're incorporated evenly.
Pack contents into a half-gallon or one-gallon glass jar or ceramic crock (food-grade plastic containers are also acceptable.) Or pack into several wide-mouth quart-sized jars. Leave 1 to 1 1/2" of head space if using wide mouth jars.
Make sure to pour every last drop of brine that formed in the bowl.
Pack down contents so that surface is even and flat.