Split the vanilla dough in half. Place one half of the vanilla dough on a piece of plastic wrap. Roll it so it forms a log with a 1 1/4" diameter.
Sandwich the matcha dough between two sheets of plastic wrap, and a rolling pin to roll it out to a rectangle as long as the vanilla log and wide enough to fully wrap around it (it'll be about 1/4" thick).
Wrap the matcha dough around the vanilla dough log. Use your fingers to smooth out the crease formed. Cover the entire log in plastic wrap and refrigerate for 15 minutes.