Prepare the peach puree: In a medium saucepan, combine the chopped peaches, 1/2 cup sugar, and lemon juice. Cook over medium heat, stirring occasionally, until the peaches soften and the mixture thickens slightly, about 10-12 minutes. Remove from heat and let cool slightly.

Blend the peach mixture until smooth. You may leave a few small chunks if preferred for texture. Transfer the puree to a bowl, cover, and chill completely in the refrigerator for at least 2 hours (or until very cold).

Make the ice cream base: In a separate large bowl, whisk together the heavy cream, whole milk, 3/4 cup sugar, vanilla extract, and salt until the sugar is fully dissolved. Be careful not to over-whip; this should not be whipped cream yet.

Combine the base and puree: Gently fold the chilled peach puree into the cold dairy base until just combined. Ensure the mixture is thoroughly chilled before churning (another hour in the fridge helps).

Churn the ice cream according to your ice cream maker's manufacturer instructions. This usually takes between 20 to 30 minutes, until the mixture thickens to a soft-serve consistency.

Transfer the churned ice cream to an airtight, freezer-safe container. Press a piece of parchment paper or plastic wrap directly onto the surface to prevent ice crystals. Freeze for at least 4 hours, or until firm, before serving.