In a medium saucepan, heat the milk and heavy cream over medium heat until it's almost simmering. Do not boil!
Remove from the heat, add the fresh mint leaves, and let steep for 10 minutes to infuse the flavors.
Strain the milk mixture to remove the mint leaves.
In a separate bowl, whisk the egg yolks and sugar together until pale and creamy.
Gradually whisk a small amount of the warm milk mixture into the egg yolk mixture to temper the eggs and prevent them from curdling.
Pour the entire mixture back into the saucepan and cook over low heat, stirring constantly, until it thickens slightly. It should coat the back of a spoon.
Remove from the heat, then stir in the vanilla extract and a pinch of salt. Let it cool completely.
Meanwhile, blend the fresh strawberries until smooth, then strain through a fine-mesh sieve to remove the seeds.
Combine the strawberry puree with the cooled custard base.
Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions.
If you don't have an ice cream maker, pour the mixture into a shallow dish and place it in the freezer. Every 30 minutes, stir with a fork to break up any ice crystals. Repeat this for 3-4 hours.
Before serving, let it sit at room temperature for a few minutes to soften slightly.
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