Place 1 cup of the french cream in a medium bowl. Set aside.
Add 1/2 cup french cream, dripped yogurt, honey, and salt to a medium saucepan.
Split the vanilla beans lengthwise and scrape into the saucepan. Toss the pods in as well.
Stir to combine the ingredients. Cook over medium heat until it is steaming and bubbling around the edges.
While the yogurt mixture is heating, whisk the egg yolks until smooth.
Once the yogurt mixture is bubbling around the edges of the saucepan, transfer 1 cup of it to the whisked egg yolks. Stir till combined.
Transfer back into the saucepan and stir to combine. Continue to cook on medium heat until it coats the back of a wooden spoon (you should be able to swipe your finger across it and the streak will remain there).
Pour through a fine mesh strainer (this removes the vanilla bean pods) into the medium sized bowl with the 1 cup of french cream. Add a 1/2 to 1 teaspoon vanilla extract and mix until everything is well blended.
Cool in an ice bath until the mixture reaches room temperature.
Cover and chill for at least 4 hours.
Churn according to your ice cream maker's directions.