Wash and cut pears into slices. Place them in clean glass jar. Cover the pears with apple cider vinegar and close the jar tightly. Place in a cool dark place, such as a cabinet, and let sit for at least two weeks. Shake the jar slightly every other day.
When ready strain the pears out and discard them. Measure 4 parts flavored vinegar to 3 parts sugar. Bring mixture to a boil, reduce and simmer for 10 minutes. Place into a clean mason jar for storage.
If tightly sealed, the syrup will last up to 6 months.
Add all ingredients to shaker tin, except cider. Dry shake to emulsify egg white. Add ice and shake hard. Add cider and double strain into a coupe glass. Garnish with cinnamon tincture and dried pear chip.