If making homemade pistachio syrup, combine the sugar, 2 tablespoons water, and chopped pistachios in a small saucepan over medium heat. Simmer for 5 minutes, then strain out the pistachios and let the syrup cool.
Sift the matcha powder into a small bowl or mug to remove any clumps.
Add the 2 tablespoons hot water and whisk vigorously with a bamboo or small regular whisk until a smooth, lump-free paste forms.
Heat and froth the milk using a milk frother or steam wand until hot and foamy, or heat in the microwave and froth with a handheld frother.
Pour the pistachio syrup into your serving mug, add the matcha paste, and stir to combine.
Pour the frothed milk over the matcha mixture, holding back the foam with a spoon, then spoon the foam on top. Serve immediately.