Prepare your ice cream bowl according to the manufacturer’s instructions by chilling it for 24 hours beforehand or however long is recommended. If you have the option to change the freezer’s temperature, it should be at least -18 C or -.4 F. If you can get it even colder, that’s even better as it ensures the freezer bowl will be as frozen as possible.
In a large bowl, whisk together the egg yolks and 1/4 cup of the sugar until the mixture is well combined and a bit lighter (ignore that it says 3/4 cup below - it's a technical issue I can't change).
4 large egg yolks, 3/4 cup (150 grams) granulated sugar
In a medium saucepan, mix together the remaining 1/2 cup sugar, milk, 1/2 cup of heavy cream (ignore that it says 2 cups below - it's a technical issue I can't change), lime zest, and just 1/8 teaspoon salt. Heat the mixture over medium heat until very hot and steamy.
1 cup (236 ml) whole milk, 2 cups (473 ml) heavy cream, 2 tablespoons finely grated lime zest, 1/8-1/4 teaspoon salt
While it's heating up, pour the remaining 1 1/2 cups of heavy cream into a large mixing bowl. Set a fine-mesh sieve over the mixing bowl.
Slowly pour the hot milk mixture over the whisked yolks to temper the eggs. Whisk continuously until smooth, then return the mixture to the hot saucepan.
Using a wooden spoon, stir the mixture constantly over medium-low heat on the stove until the mixture thickens slightly, coats the back of the spoon, and reaches 170 °F (77 °C).
Pour the mixture through the strainer, using a silicone spatula to press down on the lime zest caught by the strainer to get out as much liquid as possible.
Taste and add another 1/8 teaspoon or even more salt, if desired.
Let cool for about 30 minutes at room temperature, cover with plastic wrap and refrigerate for at least 8 hours, or overnight, until thoroughly chilled.
Mix in the lime juice just before churning.
1/2 cup (118 ml) freshly squeezed lime juice
Pour the mixture into the totally frozen ice cream bowl and churn according to the manufacturer’s instructions. The ice cream will be like soft-serve straight from the machine.
Scoop into a freezer-safe container and freeze for 4 hours to help it firm up. Overnight, it gets pretty firm but was soft enough to scoop about sitting at room temp for about 5 minutes.