Using a small food processor, small blender or an immersion blender, puree the mango until homogeneous. You can also mash the mango with a fork or potato masher by hand, though the puree will be a lot chunkier. If you want something smoother, press the mango through a strainer.
Then, make the matcha. In a matcha bowl (or any small bowl), whisk together the hot water and matcha until the are no more clumps of matcha, and the mixture is bubbly.
Mix the sugar and salt into the matcha, and stir until dissolved. You may need to add more or less sugar, depending on how sweet your mango is (I would recommend tasting your mango now and making adjustments to the matcha).
Spoon the mango puree into your serving glass, then add enough ice to fill your glass one third to half full. Pour the milk on top, then slowly add the matcha on top (in these pictures, the matcha sunk below the milk, but it was added last I promise).
Give the drink a good mix before sipping.
You can use fresh or frozen chopped mango, or even canned mango puree. I would not recommend mango juice, since it isn’t as flavorful.
Any kind of milk is fine, as long as you find it creamy to your taste.