In a medium bowl, combine the sliced peaches, 1/2 cup sugar, and lemon juice. Toss gently and let macerate for 30 minutes at room temperature, stirring occasionally. The peaches will release their juices and soften slightly.

Transfer half of the macerated peaches with their juices to a blender or food processor and puree until completely smooth. Dice the remaining peaches into 1/4-inch pieces and set aside in the refrigerator.

In a medium saucepan, combine the heavy cream, milk, and remaining 1/2 cup sugar over medium heat. Stir occasionally until the mixture is steaming and the sugar has dissolved completely, about 5 minutes. Do not let it boil.

In a separate bowl, whisk the egg yolks until smooth. Slowly pour 1 cup of the hot cream mixture into the yolks while whisking constantly to temper them. This prevents the eggs from scrambling.

Pour the tempered egg mixture back into the saucepan with the remaining cream. Cook over medium-low heat, stirring constantly with a wooden spoon, until the custard thickens enough to coat the back of the spoon, about 5-7 minutes. It should reach 170-175°F on an instant-read thermometer.

Remove from heat and immediately strain the custard through a fine-mesh sieve into a clean bowl. Stir in the peach puree, vanilla extract, and salt until fully incorporated.

Cover the bowl with plastic wrap, pressing it directly onto the surface of the custard to prevent a skin from forming. Refrigerate for at least 4 hours or overnight until thoroughly chilled.

Pour the chilled custard into your ice cream maker and churn according to manufacturer's instructions, typically 20-25 minutes, until it reaches soft-serve consistency.

During the last 2 minutes of churning, add the reserved diced peaches and let them incorporate. Transfer the ice cream to an airtight freezer-safe container, press plastic wrap on the surface, and freeze for 4-6 hours until firm enough to scoop.