1. Muddle orange slice, brown sugar cube, and Angostura bitters in a cocktail shaker to release flavors.
2. 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.
3. Top with sparkling apple cider. Garnish with orange peel and fresh thyme sprig.