1. In a food processor or blender, puree peaches wtih lime juice until smooth. Push puree through a fine sieve to remove any tough pieces of skin. Set aside.
2.In a bowl, whisk egg yolks with sugar until thickened and pale yellow. Set aside.
3. In a medium saucepan over medium-low heat, bring cream and milk to a simmer. Gradually whisk into the egg mixture.
4. Return entire mixture to the saucepan. Cook over low heat, stirring constantly, until the mixture is thick enough to coat the back of a wooden spoon. Be careful not to let it boil. Strain into a clean large bowl. Let cool to room temperature.
5. Stir in peach puree and vanilla. Cover and refrigerate until completely cold or overnight.
6. Transfer to an ice crema maker and freeze according to manufacturer's instructions.