Add the lime juice and 3 cups water to a large pitcher.
Place the parsley, peppermint, basil and mustard seeds in a blender with the remaining 1 cup water. Puree until smooth, about 1 minute.
Strain the pureed mixture through a fine-mesh sieve into the pitcher. Refrigerate for at least 1 hour before serving. Garnish with lime slices and more parsley and mint.
Photograph by Ngoc Minh Ngo
Recipe adapted from the book Cool Waters (Harvard Common Press) for Food Network Magazine