Wash a wide-mouth 1-qt. canning jar and lid in hot, soapy water and rinse well. Set a round metal rack or a few biscuit cutters in a stockpot, fill with water, and bring to a boil. Lower jar into water, add lid with ring, and boil for 10 minutes. Reduce heat to a simmer and keep jar and lid in water until needed.
In a nonreactive saucepan, heat 3/4 cup water and vinegar with sugar, peppercorns, vanilla bean halves, 2 sprigs tarragon, and lemon zest over medium-high heat until sugar has dissolved, 5 minutes. Meanwhile, set a wide-mouth funnel in jar and fill with cherries to shoulder of jar.
Pluck 2 strips lemon zest and vanilla bean halves from pan and tuck into cherries (discard tarragon). Carefully pour brine with peppercorns over cherries until they are covered, leaving about 1 in. airspace at top of jar. Tuck in fresh tarragon. Run a knife around inside edge of jar to release bubbles.
Close the lid just until tight. Let the pickles cool to room temperature, and then chill at least overnight before eating and preferably 1 week.
Make ahead: Up to 6 months, chilled.