Place the cream, milk, and sugar in a small heavy saucepan over medium heat. Cook until very hot but not boiling (the milk should bubble around the edges and start steaming), stirring frequently.
Beat the egg yolks in a small bowl.
Temper the egg yolks: slowly whisk 1/2 cup of the hot milk-cream mixture into the bowl with the egg yolks.
Turn the heat to low and pour the tempered yolks-milk combination back into the pot. Cook, stirring constantly, just until the mixture thickens slightly and coats the back of a spoon, about 5 minutes. Pour through a metal sieve into a heatproof bowl. Let cool, either by setting the bowl in a larger bowl filled with ice, or by covering and placing in the fridge for several hours.
When cold, beat the yogurt with a fork until smooth. Pour about 1/2 cup of the custard mixture into the yogurt, beating as you go. Slowly pour the rest in.
Pour the custard mixture into an ice cream maker and churn according to manufacturer’s directions. Scrape into a storage container, smooth the top, cover, and place in the freezer. Freeze for 4-6 hours before scooping and serving.