TURMERIC PASTE - Combine the the turmeric and water in the small saucepan and bring to a boil. Reduce heat and simmer until the mixture forms a thick paste. Allow to cool, then transfer to a storage container.
TEA - Bring the water and lemongrass to a boil in the 2 quart saucepan. Boil 5 minutes, then remove from heat. Add the tea bags and steep for 20 minutes. Strain the mixture to remove the lemongrass and tea bags. Add the honey and turmeric past, and stir to dissolve. Allow the tea to cool to room temperature and strain into the pitcher through a coffee filter and stir in the vanilla extract. Mix the half and half and coconut milk in the liquid measuring cup until well blended.
To serve, pour 1 cup tea mixture over ice in 4 tall glasses, then add 3 tablespoons milk mixture to each glass. Serve with the milk floating on top and allow each person to stir as desired.