In a medium saucepan combine the cream, milk and orange zest and bring to a light boil. Remove the pan from heat, cover, and let stand while you make the other mixture.
In another saucepan, combine ½ cup sugar and orange juice and bring to a boil over medium high heat, stirring with a whisk until sugar is dissolved. Bring to a boil without stirring, but swirling the pan every so often. Do this until the the mixture turns into a deep caramel color.
Remove the caramel from heat and carefully add the warmed cream mixture together, while whisking until smooth. Put back on low heat, while whisking for a few more minutes.
In a separate bowl, whisk together the egg yolks, ¼ cup sugar and salt. Slowly heat about ½ cup of the warm cream mixture to the eggs while whisking. You want to do this slowly to "temper" the eggs so they don't scramble and everything incorporates well. So this until everything is mixed together.
Bring mixture back into the saucepan and cook on low heat while stirring with a wooden spoon. The custard will thicken and you want to be able to coat the back of the spoon.
When ready, pour mixture through a fine sieve and into a clean bowl. Stir in vanilla and allow to cool to room temperature. Then place in refrigerator for at least 2 hours until cold.
When custard is cool enough, pour into your ice cream maker (I used my Kitchen-Aid attachment). Leave it on setting 1-2 for 20 minutes. At this point it was way too soft and I placed it in an airtight container and allowed it to freeze for a few more hours. The ice cream is silky and soft enough to scoop out easily.
Notes
Burnt Orange Ice Cream Recipe adapted from Lottie + Doof