Combine the sugar and water together in a saucepan. Bring to boil over medium heat, stirring to dissolve the sugar completely. Boil for five minutes.
Add the orange juice and set aside to cool.
Pour the half and half into a small saucepan and warm over medium heat until foamy and the temperature is about 180-degrees, “scalding” the half and half.
Place the egg yolks in a small mixing bowl and whisk lightly. Ladle about ¼ cup of the hot half and half into the egg yolks, whisking to blend together, tempering the egg yolks. Continue adding the hot half and half until you’ve added about half in with the eggs.
Return the tempered egg yolks to the saucepan and cook over medium heat until thickened, about 18 to 20 minutes. Stir constantly to prevent the custard from scorching or lumping.
When the mixture has thickened remove the pan from the heat and stir in the simple syrup, the orange zest and the orange oil. If it looks a bit “lumpy” don’t worry – it will blend perfectly in your ice cream maker.
Pour the orange simple syrup and the custard base into a heatproof container. Allow the custard to cool slightly, then cover and refrigerate until chilled – about 3 to 4 hours or overnight.
When you’re ready to make the sherbet, pour in the remaining cup of heavy cream and give the custard a quick stir then pour it into an electric ice cream maker for about 30 to 40 minutes.
Transfer the sherbet to a freezer-proof container and freeze until firm.