Score an x on the bottom of each peach. Bring a medium pot of water to a boil and set aside a bowl of ice water. Dip each peach into the boiling water for 30 seconds then remove and plunge immediately into ice water. Remove, slide the skin off and set aside. Repeat with the remaining peaches.
Pit and coarsely chop the peaches. Pour out the water and add the peach chunks to the saucepan. Stir in the 1/2 cup water and 1/2 cup sugar. Using a mortar and pestle, crush the lavender and stir into the peach mixture. Bring to a simmer, cooking for about 10 minutes or until the peaches are softened. Allow the peaches to cool then puree in a food processor. Strain through a fine-meshed sieve to remove bits of lavender and any fibers from the peaches. Cool to room temperature or refrigerate overnight.
Add the whole milk and cream to a large saucepan. Heat on medium temperature until the edges of the milk begin to slightly bubble. Meanwhile, whip 1/4 cup sugar and 4 egg yolks in a mixer fitted with a whisk attachment. Beat until light and frothy.
Once the milk and cream has heated, with the mixer running on low, slowly pour in about 1/4 cup of the warm milk mixture into the yolk mixture. Use a small measuring cup and pour down the side of the metal mixing bowl to allow the milk to cool as it is added. Continue to gradually incorporate all of the milk.
Once blended, pour the egg yolk and milk mixture back into the saucepan. Heat on medium temperature until it just begins to thicken, coats the back of a wooden spoon, or begins to gel a bit. Remove from heat and strain through a fine sieve to remove any bits of egg. Cool completely or refrigerate overnight.
Combine together the peach mixture and the milk mixture thoroughly. Pour into an ice cream machine and turn on as instructed for your machine. My machine is quite small so I divided the batch into two portions, cleaning and freezing the ice cream/gelato mixer container between batches.
Notes
Gelato is meant to serve quite soft to allow the flavors to be heightened. You may wish to make both the peach puree and milk mixture the day before, then blend and serve immediately. Alternately, you can make the gelato ahead, freeze then thaw in the fridge for a while before serving in order to soften it to the right consistency.
Recipe by Just a Smidgen at https://justasmidgen.com/2013/05/26/when-in-rome/