Combine the diced peaches, 1/2 cup sugar, and lemon juice in a small saucepan. Cook over medium heat for about 5 minutes, stirring occasionally, until the peaches are slightly softened and the sugar is dissolved. Remove from heat and let cool slightly.

In a separate medium saucepan, whisk together the milk, 1 cup of heavy cream, the remaining 1/2 cup sugar, and salt. Heat over medium heat until the mixture is steaming and small bubbles form around the edges (do not boil).

In a bowl, whisk the egg yolks until pale. Slowly temper the hot milk mixture into the yolks, whisking constantly. Pour the tempered yolk mixture back into the saucepan.

Cook the custard base over low heat, stirring constantly with a rubber spatula, until the mixture thickens enough to coat the back of a spoon (reaching about 170°F/77°C). Do not allow it to boil. Remove from heat and stir in the vanilla extract.

Strain the custard base through a fine-mesh sieve into a clean bowl to remove any cooked egg bits. Stir in the cooled peach mixture. Place the bowl over an ice bath and stir occasionally until cooled completely, about 30 minutes.

Once chilled, stir in the final 1 cup of cold heavy cream. Cover the custard and chill in the refrigerator for at least 4 hours, or preferably overnight, until very cold.

Churn the cold mixture in an ice cream maker according to the manufacturer's directions until it reaches a soft-serve consistency. Transfer to an airtight container and freeze for another 2-4 hours to firm up before serving.