Second attempt at this one. In the blender I used 1 cup of 2% milk. 2 oz of vanilla yogurt (per Lala’s suggestion), 2 packets of Splenda, a small tray of shaved ice (about 1 cup), and 1/2 tsp of tea powder.
The addition of the yogurt really helps as did cutting down the amount of powder. It still tastes a little like I imagine a protein powder drink tastes but much improved. It is very thick and creamy. It is not quite a replacement for my green tea frappe but I will definitely do this again. Next time I may use banana yogurt.