Blend all ingredients using an immersion blender until smooth.Use a tall container so there isn't a mess. Pulsed on low for a few seconds until everything was blended together. The ice cream is just the right consistency when it's somewhat soft and easy to scoop but not runny.
The color of the matcha tells you the quality of matcha. The brighter the green it is, the more expensive. Use matcha in the $20-$50 range to get a nice green color. The cheaper matcha will be brownish in color and make your milkshake look muddy.
If you don't have an immersion blender, a regular blender will work too.
Don't use rock hard ice cream since it'll be too much work for the blender. Wait a few minutes after taking the ice cream out of the freezer and let it soften a bit before blending.
The perfect milkshake formula is 3 scoops of ice cream for every 1/4 cup of milk.