Combine the water, brown sugar, pumpkin purée, cinnamon, ginger, nutmeg, cloves, and salt in a small saucepan.
Bring to a gentle simmer over medium-low heat, whisking until the sugar dissolves and the pumpkin is completely incorporated. Reduce the heat and simmer gently for 5–7 minutes, stirring occasionally, until fragrant and slightly thickened.
Strain
Remove from the heat and pour the syrup through a fine-mesh strainer into a jar. Press gently with the back of a spoon to extract the syrup, but don't force all of the pumpkin solids through.
Set aside. The syrup will thicken slightly as it cools.
Brew the Guayusa
Bring 1 1/2 cups water to just below a boil. Add the guayusa tea and steep for 7 minutes for a strong brew that can stand up to the pumpkin syrup and milk.
Remove the tea bags.
Build the Lattes
Divide the hot guayusa between two serving glasses or mugs. Stir 1 1/2–2 tablespoons Pumpkin Spice Syrup into each mug, adjusting to taste.
Iced (optional)
For an iced latte, skip the mug and fill a glass about 3/4 full with ice, then pour the hot guayusa and syrup mixture over the ice to cool it as you pour.
Froth the Milk (warm version)
Warm the milk until steaming, then pour it over each latte.
Froth the warm cream with some more pumpkin spice syrup (to taste), and turmeric (optional), then spoon the foam over the top.
Cold Foam (iced version)
Pour the cold milk into the iced tea
Froth the cold cream with some more pumpkin spice syrup (to taste), and turmeric (optional)
Finish with a dusting of cinnamon or freshly grated nutmeg and serve immediately.
Notes
The Pumpkin Spice Syrup can be made ahead and refrigerated in an airtight container for about 1 week. Shake or stir before using. A little natural separation from the pumpkin is normal.