Sift the matcha. Place a fine-mesh sieve over your mug and push the matcha through with the back of a spoon — this breaks up lumps before they can form.
Heat the water. Bring fresh water to about 175°F (80°C), just below a simmer. Boiling water scorches matcha and brings out bitterness. No thermometer? Let a boiled kettle sit 2–3 minutes.
Whisk. Pour the hot water over the matcha and whisk briskly in a zigzag motion for 15–20 seconds until frothy with fine bubbles. A bamboo whisk is traditional; a small wire whisk or frother works too.
Warm and sweeten the milk. Heat the dairy-free milk until steamy, not boiling, then stir in the maple syrup or honey until dissolved.
Combine. Pour the whisked matcha into a mug, add the warm milk, and stir gently once or twice. Taste and adjust sweetness.
For iced: Skip warming. Fill a tall glass with ice, add cold milk, then pour the whisked matcha over the top. Stir before drinking.