Put cranberries, sugar, orange juice, and orange peel in saucepan. Bring to a simmer. Cook until cranberries have popped and softened, about 10 minutes.
Purée mixture with immersion blender, in food processor, or in blender.
Whisk butter into warm liquid.
Put eggs and yolks into a bowl. Beat lightly. Slowly whisk a cup of the warm cranberry liquid into the eggs to temper them, then combine both and whisk them together.
Return mixture to pot. Cook over low heat until nearly bubbling and thickened, approximately 10 minutes.
Cool to room temperature. If preparing curd ahead of time, press plastic wrap on top of curd and refrigerate for up to 1 day.