Make a slurry by combining the water and cornstarch in a small dish and setting it aside. Coarsely chop the peaches into ½ inch pieces.
Make the syrup:
In a medium saucepan, add the peaches, sugar (or honey), and the liquid from the can to a boil. Stir occasionally. Reduce the heat and simmer for about 10 minutes.
Add the slurry, simmer for 1 minute, and turn off the heat. Let the peach syrup sit in the pot for 5 minutes
Transfer the mixture to a blender and blend until smooth.
Store:
Store in an airtight container or jar in the refrigerator for up to two weeks. Take it out a few minutes before serving at room temperature or warm it the microwave.
Notes
With fresh peaches: substitute the canned peaches with 2-3 peeled and sliced peaches (about 2 cups) + 1 cup water + ¼ cup honey or sugar.