Muddle orange slice, brown sugar cube, and Angostura bitters in a cocktail shaker to release flavors.
Fill shaker with ice cubes, and add cognac; cover with lid, and shake vigorously until thoroughly chilled (about 30 seconds). Strain into a stemmed 10-oz. glass.
Top with sparkling apple cider. Garnish with orange peel and fresh thyme sprig.
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