Peel and slice peaches, then toss in a large bowl with 1/2 cup of the sugar and lemon juice to combine. Let sit at room temperature for 30 minutes to an hour, until the peaches are soft and have released their juices to create a syrupy liquid.

Once the peaches have released their juices, mash them with a fork or potato masher until only very small chunks of peach remain. You don't want large, individual pieces of peach in your ice cream or they will freeze very hard. Strain the juice into a separate bowl, reserving both the liquid and the mashed peaches and refrigerating until ready to use.
Meanwhile, in a medium saucepan, stir together the cream, milk, another 1/2 cup of the sugar, and the salt. Heat over medium-low heat until hot, but not bubbling.

In a large bowl, whisk together the egg yolks and remaining 1/4 cup of sugar, until light in color, about two minutes. 

While whisking, slowly pour in 1/2 cup of the hot cream mixture into the egg yolk and sugar mixture to temper the eggs before adding them to the custard base. Slowly add another 1/2 cup of hot cream, whisking the entire time.

Pour the egg yolks mixture into the saucepan with the rest of the custard base and stir gently with a wooden spoon for 2-4 minutes, or until the mixture is just thick enough to coat the back of the spoon. Remove from heat and stir in the vanilla.

Strain the custard base through a fine mesh strainer into a clean bowl, then stir in liquid from the mashed peaches and refrigerate for 4 hours, until thoroughly chilled.

Pour peach ice cream base into ice cream maker and churn according to manufacturer's instructions, until it looks like soft-serve ice cream, about 25-30 minutes. Add the reserved mashed peaches during the last 30 seconds or so of the churning process, then transfer the ice cream to an airtight container and freeze at least 4-6 hours.