Bring milk to a boil. Remove from heat and add green tea. Mix well. In a separate bowl, beat egg yolks and sugar together until they form a ribbon. Combine egg mixture and milk, then strain into a saucepan. Cook over mediumhigh heat until just before the mixture reaches a boil. Remove from heat and cool completely over ice water. Beat heavy cream and half and half over ice water until frothy. Pour into egg mixture and mix well. Process in ice cream maker according to manufacturer's instructions. Freeze 2-3 hours before serving.