Add milk and sugar to small sauce pan and heat over medium heat until it simmers.
Add the Matcha to the sauce pan and stir with a whisk until the milk just starts to bubble. You are attempting to incorporate as much of the Matcha as possible into the milk.
Pour the milk mixture through a strainer into a bowl. If you have a large amount of tea in the strainer, put the milk and tea from the strainer back into the pot and stir it in again for a minute or two. Pour back through the strainer. There will probably be a little tea in the strainer even if you mixed it in well.
Cool the milk mixture in the refrigerator or in an ice bath.
Add the whipping cream and vanilla to the milk mixture and stir.
Cover the bowl with plastic wrap, making sure to place the plastic wrap directly onto the mixture. It should be touching the mixture because that keeps it from forming a skin.
Refrigerate for at least two-three hours and overnight if possible.
Churn ice cream according to your maker's instructions.