Prep Glass: Fill your Old Fashioned glass with ice cubes. Give it a quick stir and set it aside to chill.
Add Bitters: Pour 2 dashes of Peychaud's Bitters into the mixing glass.
Add Benedictine: Pour ½ oz Benedictine into the mixing glass as well.
Add Whiskey: Add 1 oz Irish Whiskey.
Add Mezcal: Finally, measure and add 1 oz Mezcal to the mix.
Add Ice and Stir: Fill the mixing glass with ice. Using a bar spoon or a long stirrer, stir well (for about 15-20 seconds). Give it a taste and stir a bit more if you feel like more dilution is necessary.
Serve: Discard the ice into the Old Fashioned glass and refill it with fresh, new ice cubes (you can also use the cocktail strainer to remove the excess water that has formed at the bottom of the glass and add a few more ice cubes if necessary). Using the cocktail strainer, strain the mixture into the ice-filled glass.
Garnish: Place a thin apple slice into the glass for garnish and serve immediately.