The French "creme anglaise" method of ice-cream making gives ice cream a rich, voluptuous flavor and texture.
In a nonreactive pan, combine the milk, 1/2 cup of the cream, the sugar, and the grated zest of 1 lemon and 1 lime. Heat the mixture, without letting it boil, just until the sugar is dissolved, about 8 to 10 minutes. Set the pan aside for 10 minutes.
Whisk together the egg yolks, and slowly whisk in milk-and-cream mixture. Return to pan and cook over a low flame, stirring with a wooden spoon, until mixture thickens to a custardlike consistency, about 8 minutes. Do not let it get too hot or the eggs will curdle.
Pour through a strainer into a large nonreactive bowl. Add the grated zest of the remaining lemon and 2 limes. Let stand for 10 minutes. Squeeze all the lemons and limes; add 3/4 cup of the combined juices and the remaining 3 cups cream. Chill, then pour into an ice-cream maker and freeze according to manufacturer's instructions.