Sift the matcha powder through a fine-mesh sieve into a wide bowl, pressing small lumps through the mesh with the back of a dry spoon.
Heat the measured water to 175°F (80°C). Pour it over the sifted matcha and whisk vigorously with a bamboo whisk or handheld frother for 20 to 30 seconds, until no dry specks or lumps remain at the bottom of the bowl.
Stir in the maple syrup, sweeping the bottom of the bowl to fully incorporate it. Check again for any dry green pockets before proceeding.
Warm the milk in a small saucepan over medium-low heat for 2 to 3 minutes, stirring, until it reaches 140 to 150°F (60 to 65°C). Remove from heat before it boils.
Froth the warm milk for 10 to 20 seconds with a handheld frother just below the surface to create a shallow layer of fine bubbles.
Pour the matcha tea into a 10 to 12 oz mug first, then add the warmed milk. Stir gently and spoon any remaining foam on top. Serve immediately.