Preheat the oven to 275° and position racks in the upper and lower thirds. Line 2 large baking sheets with parchment paper. In a food processor, combine the ground almonds with the matcha powder and confectioners' sugar and process until fine. Add 2 of the egg whites and the almond extract and process to a paste. Scrape the paste into a large bowl.
In a small saucepan, combine the granulated sugar with the water and cook over moderately high heat until the syrup reaches 225° (soft ball stage) on a candy thermometer. Meanwhile, in the bowl of a standing electric mixer fitted with the whisk, beat the remaining 2 egg whites until soft peaks form. With the machine at medium-high speed, gradually drizzle in the hot sugar syrup and beat the meringue until it is stiff, glossy and just warm to the touch, about 4 minutes. Using a large rubber spatula, fold the meringue into the matcha-almond paste until no streaks remain.
Spoon the meringue into a pastry bag fitted with a 3/4-inch round tip. Pipe about ten 2 1/2-inch rounds of the meringue onto each of the prepared baking sheets. Using a moistened fingertip, carefully smooth the tops. Let the macarons stand uncovered for 15 to 20 minutes; this will make the surfaces shiny and crisp.
Bake the macarons for 30 minutes, until the tops and bottoms are dry and crisp; shift the baking sheets from top to bottom and front to back halfway through baking. Prop the oven door open several inches and let the macarons cool completely.
Working in batches, scoop 10 scant 2-tablespoon mounds of each ice cream onto a sheet of wax paper. Using a spatula, lightly flatten the ice cream and sandwich a scoop each of vanilla and green tea ice cream between 2 macarons; press very lightly to close. Serve right away.