In the bowl of a food processor, process sugar with whole cranberries and orange zest until cranberries are finely chopped and well incorporated into the sugar, about 7-10 pulses.
Pour cranberry mixture into a large bowl with softened butter. Beat on low so as not to splatter everywhere. Add the eggs, one at a time, until incorporated. The mixture will look very curdled and there may be little bits of butter throughout. This is totally okay and expected.
Pour the whole thing into a medium saucepan and whisk continuously over medium heat until mixture begins to thicken. This will take anywhere from 5-10 minutes. It should be about as thick as mayonnaise when it's done.
Immediately remove the pan from the heat and pour the cranberry curd into a fine mesh sieve set over a medium bowl. Press through sieve with the back of a spoon or spatula to remove all the seeds and pulp of the cranberries, and discard this.
Place plastic wrap directly on the surface of the curd and chill the curd for at least 2 hours, or up to one week.