Zest the orange, then juice it and set aside.
In a medium saucepan, combine the milk, heavy cream, sugar, and cocoa powder. Heat over low heat, stirring until the sugar is dissolved.
Add the finely chopped dark chocolate and stir until completely melted and smooth.
In a separate bowl, whisk the egg yolks. Gradually add a little of the hot chocolate mixture to temper the eggs, whisking constantly.
Pour the tempered egg mixture back into the saucepan and cook over low heat, stirring constantly, until the mixture thickens slightly (about 5 minutes).
Remove from heat and stir in the orange zest, orange juice, and vanilla extract. Let cool to room temperature.
Pour the cooled mixture into an ice cream maker and churn according to the manufacturer's instructions until creamy.
If you don't have an ice cream maker, pour the mixture into a shallow container and place it in the freezer. Stir every 30 minutes to prevent ice crystals from forming.
Once the ice cream is completely frozen (after about 4-5 hours of freezing), serve garnished with fresh orange zest or chocolate shavings.
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