For the spiced pear syrup, roughly chop the pears into approximately one centimeter chunks and add into a small pot along with the water, brown sugar, granulated sugar, nutmeg, cinnamon sticks, and cloves. Place the pot over medium low heat and bring the mixture to a simmer. Simmer for ten minutes or until the sugar is fully dissolved and the pears are starting to soften.
Remove the syrup from the heat and allow it to sit at room temperature until cooled to room temperature. Strain the mixture through a fine mesh sieve then place in the fridge to cool.
To make the cocktails, fill a cocktail shaker halfway with ice and add in the bourbon, red wine, spiced pear syrup, lemon juice, and egg white. Shake very well for at least 20 seconds until well chilled and foamy.
Strain the cocktail into two champagne coups and garnish with a thin slice of pear.