In a medium saucepan, combine pears, honey, and water. Bring to a soft boil. Lower to medium-low heat and simmer for 25 minutes. The pears will release their juices and soften. Remove from heat.
Add in grated ginger. Cover pan and allow to sit another 10–15 minutes so flavors can meld.
Strain mixture with a sieve, pressing pears into the sieve to extract their remaining juices. Discard pressed solids.
Add the mixture back to the pan along with apple cider vinegar and bring to a low boil, simmering 2–3 minutes. Remove from heat.
Pour mixture into an air-tight container and store in the refrigerator for up to two weeks.