Peel, core, and chop the ripe pears into small pieces, placing them in a mixing bowl.
Crush a cinnamon stick with your muddler to release its fragrant oils, then add it to the pears.
Squeeze fresh lemon juice from the lemon and pour it over the pear and cinnamon mixture. Muddle together gently until the pears are well mashed and fragrant.
Add a splash of honey syrup into the muddled mixture, stirring to combine and enhance the sweetness.
Fill a shaker halfway with ice cubes, then pour in the muddled pear mixture along with the cognac.
Secure the shaker lid and shake vigorously for about 15 seconds, until the mixture is well chilled and the flavors meld.
Place a fine strainer over chilled glasses and strain the cocktail mixture into each glass, catching any pulp or spice bits.
Garnish each drink with a cinnamon stick and a thin slice of pear for a beautiful presentation and extra aroma.
Serve immediately and enjoy the warmth, aroma, and smooth flavor of this festive cocktail.