In a large mixing bowl, whisk together the all-purpose flour, baking powder, salt, and matcha powder until the green matcha is evenly distributed throughout the dry ingredients.
In a separate medium bowl, beat the egg with a fork, then whisk in the whole milk, granulated sugar, and cooled melted butter until fully combined.
Pour the wet ingredients into the dry ingredients and stir gently with a wooden spoon until just combined; the batter should be slightly lumpy but without dry flour pockets.
Heat 2 inches of vegetable oil in a heavy-bottomed pot to 350°F, using a deep-fry thermometer to monitor the temperature.
Drop tablespoon-sized portions of batter into the hot oil and fry for 2-3 minutes per side until golden brown and puffed, flipping once with a slotted spoon.
Remove the fried matcha fritters and drain on a paper towel-lined plate for 1 minute to absorb excess oil.
Sift confectioners' sugar generously over the warm fritters just before serving for a sweet finish.