In a 3-quart saucepan, heat the milk and sugar over medium heat, stirring occasionally, until it just comes to a boil, about 4 minutes. Stir in the vanilla.

Prepare an ice bath by filling a large bowl with several inches of ice water. Put a smaller metal bowl in the ice water and set a fine strainer on top.

In a medium bowl, lightly beat the egg yolks. Pour about 1/2 cup of the milk mixture into the egg yolks, whisking constantly to prevent the eggs from curdling. Pour the egg mixture into the saucepan with the milk mixture and cook, stirring constantly with a wooden spoon, until the custard thickens slightly, enough to coat the back of the spoon, 4 to 8 minutes. Immediately pour the mixture through the strainer into the small bowl. Stir in the yogurt and zests and cool the custard completely by stirring it over the ice bath.

In a blender or food processor, purée the avocado with the lemon and lime juices and about 1 cup of the cooled custard until smooth. Fold the avocado mixture back into the custard. The mixture should be thick, creamy, and pale green. Freeze the custard in an ice cream maker according to the manufacturer’s instructions. Transfer the frozen yogurt to an airtight container and freeze until solid, at least 4 hours.