Rinse an old fashioned glass with a small amount of anise extract, swirling to coat the sides. Pour out excess - this creates the signature anise aroma without overwhelming the drink.
In a cocktail shaker filled with ice, combine the cooled tea, vanilla extract, diluted apple juice concentrate, simple syrup, and bitters. Shake vigorously for 10-15 seconds.
Fine strain the mixture into the prepared glass over one large ice cube or several smaller ones.
Express the oils from the lemon peel by holding it over the drink and giving it a firm twist. Drop the peel into the glass and garnish with fresh thyme sprig if desired.