In a medium bowl, whisk together egg yolks, milk, and vanilla extract until smooth and pale yellow.

Sift together the flour, matcha powder, baking powder, and salt into the yolk mixture. Whisk until just combined with no dry streaks, being careful not to overmix. Set aside.

In a separate large clean bowl, beat egg whites with cream of tartar using an electric mixer on medium speed until foamy. Gradually add sugar one tablespoon at a time, then increase to high speed and beat until stiff peaks form that hold their shape when you lift the whisk, about 3-4 minutes total.

Gently fold one-third of the egg whites into the matcha batter using a rubber spatula with broad scooping motions from bottom to top. Add remaining whites in two more additions, folding just until no white streaks remain. The batter should be thick, airy, and pale green.

Heat a nonstick skillet or griddle over the lowest heat setting. Lightly grease 3-inch ring molds and place them in the pan. Grease the pan surface around the molds as well.

Spoon batter into each mold, filling about three-quarters full. Add 1 tablespoon of water to the pan away from the molds, then immediately cover with a lid.

Cook for 6-7 minutes without lifting the lid, until the bottoms are golden and the tops look slightly set. Carefully remove the lid, gently lift off the ring molds using tongs, then flip each pancake with a wide spatula.

Cook uncovered for another 3-4 minutes until the second side is lightly golden and the centers spring back when gently pressed. The pancakes should jiggle slightly but hold their shape.

Transfer to serving plates immediately. Repeat with remaining batter, re-greasing molds and pan between batches and adding fresh water each time you cover.