Toast the rice: Spread the steamed rice on a baking sheet and toast at 350°F until golden. Let it cool completely, then pulse in a food processor into rough bits.
Prepare the tea: If not using tea bags, blend genmaicha until the leaves are fine but not powdered. Mix in matcha.
Infuse the butter: Melt butter in a pan, then stir in most of the tea (reserving a little more than 1/8 tsp for the sugar coating). Let the butter cool to room temperature.
Cream sugar into the butter. Add egg, vanilla extract, and salt, then beat until light and fluffy.
Combine dry ingredients: Mix together flour, cream of tartar, baking soda, half of the toasted rice, and then fold it into the butter egg mixture until it is just combined.
Portion & freeze: Scoop dough into 6 large cookies and place on a tray lined with plastic wrap. Freeze overnight.
Make the sugar coating: Mix reserved tea, 1/8 cup sugar, and the remaining toasted rice.
Coat the cookies: Place frozen dough balls in a ziplock bag with the sugar coating, seal, and shake to coat.
Evenly space the cookie dough on a prepared baking tray and let it sit at room temp for 30 minutes.
Preheat oven to 350°F and bake.
Create ripples: Once you see the cookies puff up in the oven, lift each corner of the baking pan about 4 inches from the oven rack and drop it. Repeat this 3 times as the cookies bakes and re-puffs up.
When the edges turn golden and ripples set but the center is slightly soft, remove from oven. Cool and enjoy!