In a small saucepan over medium heat, combine half the peaches with 1/2 tablespoon of the lemon juice and 1/4 cup of the sugar. Cook, stirring, until the sugar dissolves and the peaches are just heated through, about 3 minutes. Do not let the peaches disintegrate. Transfer the peaches to a medium metal bowl; reserve.
Put the remaining peaches in a bowl and sprinkle with the remaining lemon juice; toss to coat. Cover with plastic wrap and refrigerate until ready to use.
In the same saucepan over medium-high heat, bring 2 1/2 cups of the half-and-half to a simmer and remove from the heat. In a metal bowl, whisk the egg yolks, pinch of salt and the remaining 1/4 cup sugar until blended. Gradually pour the hot half-and-half into the yolk mixture, whisking constantly.
Return the mixture to the saucepan and decrease the heat to medium-low. Cook, stirring constantly with a wooden spoon, until the custard is thick enough to coat the back of the spoon, about 5 minutes. It should leave a clear trail when a finger is drawn through it. Do not allow the custard to boil.
Pour the custard through a fine-mesh sieve into the reserved cooked peach mixture. Working batches, puree the mixture in a food processor or blender until smooth. Add the vanilla and the remaining 1/2 cup half-and-half and whisk to blend. Refrigerate for about 1 hour.
Transfer the custard to an ice cream maker and freeze according to the manufacturer's instructions. When nearly frozen and the consistency of thick whipped cream, add the remaining uncooked peaches. Stir just until mixed. Transfer the ice cream to a freezer-safe container, cover and freeze until firm, at least 4 hours or up to 3 days, before serving.
Makes about 1 quart.