Bring the milk to a gentle simmer in a medium-sized saucepan.

While keeping an eye on the milk, whisk the eggs, egg yolks, and ¾ cup sugar in a bowl.

Gently whisk in ¼ cup of the warm milk, then return the egg mixture to the saucepan.

Keeping the flame low, cook, stirring with a wooden spoon until the mixture is thick enough to coat the back of the spoon, about 15 minutes.

Transfer mixture to a bowl, and fold in the whipping cream. Refrigerate until cold.

Dice the peeled peaches, then add the remaining sugar and the lemon juice. Refrigerate for two hours.

Drain the peach juice into the cream mixture, mix, and pour into the ice cream maker.

Process until the mixture starts to set and add the diced peaches.

Continue to process a few more minutes to blend the fruit and the cream mixture, then freeze until ready to enjoy.