Green snow (green tea syrup and sweet beans)

1. Put the beans and 3 cups water in a small pot. Bring to a boil.
2. Cover, turn heat to low and cook for 2 minutes.
3. Turn off the flame.
4. Let the pot sit, covered, for 1 hour.
5. Bring to a boil again.
6. Cover, turn heat to low and simmer 30 minutes.
7. Add the 5 tablespoons sugar and simmer vigorously, uncovered, for another 10 to 12 minutes.
8. Cool the beans in their liquid and then drain.
9. Combine the ½ cup sugar with ½ cup water in a small pot and bring to a boil.
10. Turn heat to very low and simmer 3 to 4 minutes.
11. Cool. Mixi in the tea. (taste as you go; add more or less tea, as you like).
12. Pile a cup of shaved ice in the center of each of four ice-cream bowls.
13. Divide syrup over the ice.