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Squeeze the juice from the oranges, you can also use bottled orange juice but freshly pressed orange juice is tastier. Heat the orange juice in a medium-sized pan on medium-high heat.
Meanwhile beat the eggs along with the sugar until it's white and fluffy. Add cornstarch and combine until it's smooth. Pour a bit of the warm orange juice into the eggs and keep on mixing.
Then also pour in the rest of the warm orange juice to the eggs and keep on stirring to prevent it from creating lumps.
Pour the mixture back into the pan and add the milk. Heat it slowly on low heat and stir with a silicone spatula to prevent it from burning. This way the eggs and cornstarch will cook so the pudding will thicken.
Keep on stirring until the mixture is quite thick. Let it cool off a bit and divide over 6 glasses or bowls. Refrigerate for at least 4 hours, preferably overnight, until the pudding is completely cold and thick.
You can serve the orange pudding with whipped cream and pieces of fresh orange, enjoy!