
Peel the peaches with a peeler, or blanch them in boiling water to peel off the skin (see recipe notes below for more tips).
Remove the pit / stone by cutting the peaches in half first, and then remove the pit.
Slice the peach flesh and set aside.
Place the peaches in a blender jug, along with the sugar and lemon juice.
Blend until you have a smooth texture. Set it aside (at room temperature or in the fridge) until needed.
In a pot, whisk together the sugar and cornstarch. Add the milk and cream, and whisk until there are no cornstarch clumps in the liquid.
Cook over medium heat (adjust the heat to a manageable level on your stove), while frequently whisking. As the milk heats up, the sugar should dissolve.
Whisk the mixture constantly as the milk starts to thicken to prevent the mixture from catching at the bottom of the pot and burning, and also from forming cornstarch clumps.
When the mixture comes to a boil / gentle simmer, lower the heat slightly and allow the mixture to simmer for about 1 minute while whisking.
Remove the mixture from the heat, and whisk in the vanilla.
Transfer the thickened cream mixture into the blender jug with the blended peach puree.
Blend until the mixture mixes well and is smooth.
Pour this homogenous mixture into prepared popsicle molds and place the lids with the popsicle sticks.
Freeze overnight for the popsicles to harden. I prefer to let them freeze for about 8 hours at least.
Unmold the popsicles once frozen, and enjoy or serve immediately.