In pan, bring water and sugar to boil, stirring until sugar dissolves. Add tea bags. Cover and let steep 15 minutes.
Discard tea bags.
Using a skewer, carefully pierce weakest hole in coconut; drain liquid, reserve. Bake coconut in 400°F oven for 15 minutes.
Break coconut with a hammer, remove flesh from shell. (Then, put the lime in the coconut and drink it all up...no, not really.)
Cut coconut meat into small pieces. In a blender
, grind in small batches. Transfer to bowl.
Strain reserved coconut liquid through a fine sieve
into a 4-cup measuring cup
, add water to make 2 c. of liquid. Bring this coconut liquor-water mixture to boil, then add it to the ground coconut.
Blend 1 minute.
Strain it through cheesecloth, combine with sugared peppermint tea. Freeze in an ice cream maker