In a heavy-bottomed saucepan, combine the heavy cream, whole milk, 0.5 cup of the granulated sugar, and salt. Heat over medium heat, stirring occasionally, until the mixture just begins to simmer gently around the edges. Remove from heat.

In a separate medium bowl, whisk the egg yolks with the remaining 0.5 cup of granulated sugar until the mixture is light in color and slightly thickened. This usually takes about 1-2 minutes of vigorous whisking.

Slowly and gradually ladle about 1 cup of the warm cream mixture into the egg yolk mixture, whisking constantly to temper the yolks and prevent them from scrambling. Pour the tempered yolk mixture back into the saucepan with the remaining cream mixture, whisking continuously. Return the saucepan to medium-low heat and cook, stirring constantly with a wooden spoon or heat-proof spatula, until the custard thickens enough to coat the back of the spoon. It should reach about 175-180°F (79-82°C). Do not let it boil.

Immediately pour the cooked custard through a fine-mesh sieve into a clean bowl set over an ice bath. Stir in the lemon zest, fresh lemon juice, and vanilla extract. Continue stirring occasionally until the mixture is cool to the touch. Cover the bowl with plastic wrap, pressing it directly onto the surface of the custard to prevent a skin from forming. Refrigerate for at least 4 hours, or preferably overnight, until thoroughly chilled.

Once the custard base is completely chilled, transfer it to your ice cream maker. Churn according to the manufacturer's instructions, usually 20-30 minutes, until the ice cream reaches a soft-serve consistency.

Transfer the freshly churned ice cream to an airtight freezer-safe container. Press plastic wrap directly onto the surface of the ice cream, then seal the container tightly. Freeze for at least 2-4 hours, or until firm, before scooping and serving.