Peel, core, and dice the pears. Transfer the pears to a medium sized saucepan and add the water and sugar. Stir to dissolve the sugar and heat over high heat until it comes to a boil. Turn down the heat to low and simmer, covered, for 10 minutes.
After 10 minutes, when the pears are soft, use a potato masher to gently break down the pears. Mash them 4 or 5 times but don't completely break them down. Add the cinnamon stick, star anise, and cloves.
Continue to simmer the syrup over low heat, covered, for another 15 to 20 minutes. Remove from the heat and let steep for up to another 30 minutes. Strain the syrup and let cool completely before using. The syrup will keep in the fridge for several weeks.
To make the cocktail:
In a cocktail shaker, add the gin, Spiced Pear Syrup, fresh lemon juice, and egg white. Add ice, then cover and shake for 10 to 15 seconds. Strain into a coupe glass and enjoy!