Heat half-and-half to boiling in a small saucepan (if using tea bags). Add tea bags, remove from heat, and let steep 5 minutes. Press liquid from bags, discard them, and let liquid cool. For fresh chamomile, just stir it into cold half-and-half.
Whisk together chamomile mixture, sour cream, salt, lemon zest, and sugar in a bowl until smooth.
Freeze mixture in an ice cream maker according to manufacturer's directions until softly frozen, about 30 minutes. Transfer to a metal bowl, stir to distribute lemon zest, and freeze airtight until firm enough to scoop, at least 4 hours and as long as 1 week.
*Grow your own, or try a farmers' market.
Note: Nutritional analysis is per serving.