In a large bowl, mix together flour, matcha, baking powder, and salt. Set aside.
In another bowl, cream together butter and sugars until light and fluffy. Mix in the eggs, vanilla, and lemon extracts until combined.
Slowly mix in the flour mixture with the butter and egg mixture until the all the flour is incorporated. Fold in the chocolate chips. Chill dough for at least 30 minutes.
When read to bake, preheat oven to 350 degrees. Use two spoons or a cookie scoop to drop balls of dough onto a baking sheet, about 2 inches apart.
Bake for 7 minutes, then reduce temperature to 325 and bake for another 5 to 8 minutes, until cookies are barely golden brown around the edges. Let cool on baking sheet for 5 minutes before transferring to a wire rack.