To make the pumpkin spice syrup, place the squash, water, brown sugar, maple syrup, 2 tablespoons pumpkin spice blend, and salt in a medium saucepan, and mix well to start to dissolve the spices in the water.
Bring the mixture to a gentle boil over medium high heat, cover, reduce the heat to medium low and simmer until the squash is fully cooked through and can easily be mashed with the side of a fork, about 20 to 25 minutes.
Turn off the heat and allow to cool for 15 to 20 minutes.
Transfer the cooked squash and all the liquid to a blender and purée until smooth. Use immediately, or store in an airtight container in the refrigerator for up to 2 weeks.
To make a hot PSL, whisk together the milk and your desired amount of pumpkin spice syrup in a small saucepan and heat over medium heat.
Pour the hot milk and pumpkin spice mixture into your favorite mug. Top with hot espresso or strongly brewed coffee and garnish with a dollop of whipped cream, if using.
To make an iced PSL, add the milk and your desired amount of pumpkin spice syrup to a glass and mix well. Add ice and give everything another stir. Slowly drizzle in the espresso, so it creates an espresso layer on top. Finish with a dollop of whipped cream, if using.
To make the spice blend, place the mace, cloves, cardamom, and allspice into a spice grinder and grind into a fine powder. Transfer the ground spices to a bowl, add the cinnamon, ground ginger, nutmeg, and pepper, and mix well.