Combine sugar and brewed espresso in a saucepan over medium heat.
Stir until sugar dissolves, then let syrup cool.
In a separate saucepan, mix sugar, water, pumpkin puree, and pumpkin pie spice.
Heat until sugar dissolves, simmering for about 5 minutes.
Brew coffee and allow it to cool.
In a bowl, melt white chocolate chips with heavy cream until smooth.
Fill glasses with ice, then pour cold coffee over it.
Drizzle with espresso syrup and pumpkin spice syrup, followed by white chocolate sauce.