Preparing the dough
In a bowl, whisk together flour, cornstarch, baking powder and salt until evenly combined.
In a separate bowl, beat softened vegan butter and sugar until creamy. You can use a stand mixer or handheld electric mixer. Then add vanilla, milk and beat again until smooth.
Add flour to the butter mixture in ½ cup increments until all the flour has been added. The dough should be soft but workable.
Remove half of the dough mixture and set aside. To the remaining dough, mix in matcha powder until smooth.
Shaping the dough
Form each ball of dough into a rectangular log, roughly 2" tall x 6" long and use your hands to make sure both are are close in size as possible. If you'd like, you can clean up the edges using a sharp knife, or use a pastry cutter to help flatten the edges. Place them on a baking sheet, cover with food wrap and refrigerate for at least an hour.
After chilling, use a sharp knife to slice the dough rectangles into 9 kong strips each. First, start by slicing the dough into 3 parts, lengthwise, then turn onto its side and cut into thirds again. You will end up with 9 strips of plain dough and 9 strips of matcha dough.
Next, re-assemble your rectangles by alternating matcha and vanilla dough strips. (Example: bottom layer should be made with matcha, vanilla matcha followed by a middle layer of vanilla, matcha, vanilla and a final top layer of matcha, vanilla and matcha). See photos for more reference.
Press your mix and match logs together and refrigerate again for about 30 minutes to firm up.
Once ready to bake, preheat your oven to 350F.
Slice the dough short-wise into nice ¼" slabs. You should have a beautiful checkered pattern. Space out evenly on a nonstick baking mat and bake for 11-12 minutes. Transfer to a cooling rack and let cool completely.