In a large saucepan, combine the heavy cream, whole milk, granulated sugar, and salt. Heat over medium heat, stirring occasionally, until the sugar dissolves and the mixture is hot but not boiling (you'll see small bubbles forming around the edges).

While the cream mixture heats, whisk the egg yolks in a medium bowl until light yellow and smooth. Slowly ladle about 1/2 cup of the hot cream mixture into the egg yolks, whisking constantly to temper them. This prevents the yolks from scrambling.

Pour the tempered egg yolk mixture back into the saucepan with the remaining cream mixture. Cook over medium-low heat, stirring constantly with a rubber spatula or wooden spoon, until the custard thickens enough to coat the back of the spoon. It should reach a temperature of 175-180°F (80-82°C). Do not boil.

Immediately remove the custard from the heat and strain it through a fine-mesh sieve into a clean bowl to remove any cooked egg bits. Stir in the vanilla extract. Set the bowl over a larger bowl filled with ice and water (an ice bath) and stir occasionally until the custard is cool. Then, cover it with plastic wrap, pressing it directly onto the surface to prevent a skin from forming, and refrigerate for at least 4 hours, or preferably overnight, until thoroughly chilled.

Once the custard is completely chilled, whisk in the fresh lemon zest and lemon juice. Give it a taste and adjust the lemon juice if you want it more tart. The flavor will mellow slightly once frozen.

Pour the chilled lemon custard base into your ice cream maker and churn according to the manufacturer's instructions, typically for 20-30 minutes, until it reaches the consistency of soft-serve ice cream.

Transfer the soft ice cream to an airtight container. Press plastic wrap directly onto the surface of the ice cream, then seal the container and freeze for at least 4 hours, or until firm, before serving. This allows the ice cream to firm up to a scoopable consistency.