In a blender or food processor, puree the peaches with 1/4 cup of the milk.
Over a large saucepan, pour the puree through a fine mesh sieve, smashing any remaining chunks of peach through the mesh. Scrape the outside bottom of the sieve where lots of the puree will gather.
Add the cream and the sugar to the puree; give it a good whisk to mix in the lumps of cream.
Put the saucepan on the stove on low heat to allow the sugar to dissolve.
Meanwhile, pour the remaining 1/4 cup of milk into a bowl or small saucepan; sprinkle the gelatin over the milk and let sit for 5 minutes or more. It will form a lovely bloom on the surface.
Increase the heat under the peach mixture, whisking occasionally; you want to bring it just to a boil.
When the mixture begins to boil, remove from heat. Add the gelatin and the vanilla and whisk briskly for a few seconds.
Allow the mixture to cool for about five minutes, then pour into ramekins. This recipe fills six 6-oz. ramekins; you can use smaller or larger ramekins, depending on how many servings you want.*
Cool at room temperature for about 1/2 hour, then refrigerate for 6-12 hours or overnight until well set.
*Regarding ramekins: I use light metal darioles because they are slightly flexible and makes removing the panna cotta a bit easier. If you use metal, don't use a metal utensil to slide around the dessert to loosen it, as it will flake off little bits of metal. I plan to try some silicone ramekins next.