In a medium bowl, mix the green tea with 1/4 cup of cream to make a smooth paste. Whisk in the honey and vanilla extract. Set that bowl aside.

In another medium bowl or glass measuring cup large enough to hold all the liquid, whisk the egg yolks with the 1/4 cup of sugar.

In a medium saucepan, pour in the remaining 2 cups of cream and 1 cup of whole milk and heat over a medium heat until it starts to steam. Do not boil the milk and cream.

When the milk and cream are hot, very slowly start to pour it it over the egg yolks while whisking constantly. Start with just a small amount (about 1/4 cup) before pouring in the rest.

When it is all mixed in, pour the custard mixture back into the saucepan set over a medium heat and stir constantly, not vigorously, with a wooden spoon until the custard coats the back of the spoon. The sound of the custard will go from very splashy and watery sounding to a thicker, sloshy sound when it is close to done. To check, run your finger through the custard and if the mark your finger made does not run together, then it is ready. It will also be steaming quite a bit. When you see that it is either done or very close to being done. Do your best to not let it boil or start to bubble.

Place a fine mesh sieve over the bowl that has the green tea and honey mixture. Pour the hot custard through the sieve to catch any bits of cooked egg.

Stir the custard and green tea mixture together so that it is fully combined. Place a piece of plastic wrap directly on the custard to avoid a skin forming on top.

Chill in the fridge at least 8 hours but preferably over night. Make sure the frozen part of your ice cream maker is in the freezer so that it is ready for the next day.

To make the ice cream, pour the chilled custard into the frozen compartment of an ice cream maker and turn your machine on. Follow the instructions for your machine for a custard-based ice cream.

Pour the frozen ice cream into an air tight container and keep in your freezer.