Combine the white sugar and cinnamon on a small plate. Dip the rim of 2 martini glasses in water, then dip in the sugar to coat.
Combine the brown sugar, pumpkin pie spice, vodka, half and half, milk, pumpkin puree, maple syrup, and vanilla extract. Add to a blender or use an immersion blender to thoroughly combine the ingredients.
Add the mixture to a martini shaker filled with ice. Shake vigorously, then strain into the prepared martini glasses.