On one small plate, add the pear juice. On another small plate, add the brown sugar and cinnamon. Dip the glasses in the pear juice and wet the rime. Then, dip the rim into the brown sugar mixture to coat. Set upright and fill glasses with ice.
Add all cocktail ingredients except for the sparkling water to a shaker or separate tall class. Muddle the thyme with a muddler or the handle of a wooden spoon. We are trying to impart the thyme flavor into the juices. Shake together with an ice cube or two and then pour into the prepared glasses. Top with sparkling water.
Garnish with a pear slice and fresh thyme sprigs.