Using a large bowl, add chopped peaches, ½ cup of sugar and lemon juice; stir until well combined. Let peaches sit for 30 minutes.

Meanwhile, pour half-and-half into a medium saucepan. Place over medium-low heat until it just begins to simmer.

Using a separate bowl, whisk together the egg yolks and remaining 1 cup of sugar until well blended.

Gradually pour the heated half-and-half into the egg yolk mixture; whisking vigorously the entire time.

Transfer this mixture back into the saucepan and cook over medium-low heat, stirring constantly, until custard thickens noticeably and coats a wooden spoon. (~4-6 minutes).

Meanwhile, using a separate bowl, whisk together the whipping cream and vanilla extract.

Once the custard mixture has thickened, remove from heat and add the whipping cream mixture; stir until well combined. Pour mixture through a fine-mesh strainer into a clean container.

Using an immersion blender (or a potato masher), lightly puree peaches so that some large chunks still remain.

Add peaches to custard and stir until well combined. Cover with plastic wrap, pressing the plastic directly onto the surface of the mixture, and refrigerate at least 1 hour, or overnight.

Pour the mixture into an ice cream maker and freeze according to the manufacturer's directions.

For a softer ice cream, serve immediately. For a harder ice cream, transfer mixture into a freezer-safe container and freeze for 3-4 hours.