Make the ice cubes: In a large heatproof bowl, combine the water, hibiscus tea, English breakfast tea, thyme and orange blossom water and let steep for 5 minutes. Add the sugar and stir until dissolved. Add the ginger ale, then strain through a fine mesh strainer into a pitcher. Pour into 1-inch square ice cube molds and freeze until solid.
Make the cocktail: In a double Old Fashioned glass, muddle the orange peel with the Averna. Add bourbon and stir briefly, then add ice cubes and stir until just chilled, about 20 seconds. Serve immediately.