Wash and pit the peaches. Slice, then add them along with the honey, lemon juice, and fresh ginger to a blender container or to the bowl of a food processor.
Blend until smooth. If using a food processor, pulse on and off until very well blended.
Taste and add more honey or more ginger, depending on your preference. Blend again.
Transfer the peach mixture to the fridge and chill for an hour or more.
With your ice cream machine set to the Sorbet setting, press Start. Pour the peach mixture through the spout, then cover with the cap. Let it churn until thickened, about 28 - 30 minutes. The sorbet will be soft. If you'd like a firmer consistency, transfer it to an airtight container and freeze for 2 hours. Let stand on the counter for 15 minutes before serving.
Notes
It's not necessary to peel peaches before blending them to make sorbet. In fact, the peach skins add a warm colour to the finished sorbet.