To make the black sesame seed powder: grind 1/4 cup sesame seeds in a high speed blender (think a Vitamix). A 5-speed blender or Magic Bullet isn't powerful enough to grind the seeds fine enough, so I'd recommend trying to look for ground sesame seeds at an Asian market if you don't have a strong blender.
Feel free to use a dollop of ice cream or sub in heavy cream if you don’t have half and half!
You can skip blending the drink and mix everything together by hand - it won’t be as homeogenous but it will still taste great (and less dishes!).
The sesame seeds will separate from the rest of the drink pretty quickly, but don’t worry. Stir/swirl it back together before you take a sip.
Feel free to sub in soy milk, light coconut milk, oat milk, etc for the cows milk if you want to keep this vegan. You can also sub in some other kind of tea for the black tea- you're looking for something a little bitter to cut through the rest of the drink.