Peel and dice the peaches into small, roughly half-inch pieces. Place in a medium bowl and sprinkle with 1/4 cup sugar and lemon juice. Stir gently, cover, and let sit at room temperature for 30 to 45 minutes until syrupy.
In a medium saucepan, combine heavy cream, whole milk, and salt. Warm over medium heat until steaming with small bubbles forming around the edges, but do not boil. Remove from heat.
In a large heatproof bowl, whisk the egg yolks with remaining 1/2 cup sugar until pale yellow and slightly thickened, about 1 to 2 minutes.
Slowly pour about 1/2 cup of warm cream mixture into the egg yolks while whisking constantly. Continue adding the remaining warm cream in a slow, steady stream, whisking constantly until fully incorporated.
Pour the tempered egg mixture back into the saucepan. Cook over medium-low heat, stirring constantly with a rubber spatula, until custard thickens enough to coat the back of a spoon, about 5 to 8 minutes, or until it reaches 170 to 175°F on an instant-read thermometer. Do not let it boil.
Pour the custard through a fine-mesh strainer into a clean bowl. Stir in vanilla bean paste. Cover with plastic wrap pressed directly onto the surface to prevent a skin from forming. Refrigerate for at least 4 hours, or overnight.
Transfer the macerated peaches and their syrupy juices to a food processor or blender. Pulse 3 to 4 times to break the peaches down, leaving some small chunks for texture.
Stir the pureed peaches into the chilled custard base until fully combined. Pour into your ice cream maker and churn according to manufacturer's instructions, usually 20 to 25 minutes, until it reaches a soft-serve consistency.
Transfer the churned ice cream into a freezer-safe storage container. Smooth the top with a spatula, cover tightly, and freeze for at least 2 hours before scooping for a firmer, scoopable texture.