In a saucepan over medium heat, warm the milk and heavy cream until they begin to steam, but do not boil.
In a separate bowl, whisk together the egg yolks and sugar until pale and fluffy.
Slowly pour the warm milk mixture into the egg yolk mixture, whisking constantly to prevent the eggs from curdling.
Pour the mixture back into the saucepan and cook over low heat, stirring constantly, until it thickens slightly (about 5-7 minutes). Do not boil!
Strain the mixture through a fine-mesh sieve, then stir in the lemon juice, lemon zest, and vanilla extract. Let cool to room temperature.
Refrigerate the ice cream base for at least 4 hours, or preferably overnight, to chill thoroughly.
Pour the mixture into an ice cream maker and churn until it reaches a creamy consistency (about 20-30 minutes).
If you don't have an ice cream maker, pour the mixture into a freezer-safe container and stir every 30 minutes with a fork or whisk to prevent ice crystals from forming.
Once the ice cream has reached the desired consistency, serve immediately, or transfer it to an airtight container and freeze for an additional 2-3 hours to achieve a firmer texture.
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