With a vegetable peeler, pare green part of peel from 4 limes. Put peel and sugar into a food processor and whirl until peel is very finely chopped; let stand, covered, at least 30 minutes. Ream juice from lime. Measure 1 cup; save the remainder separately.
Add the 1 cup lime juice to the sugar mixture in food processor; whirl until sugar dissolves. Pour mixture through a fine strainer into a 2- to 3-quart pan, pressing liquid from peel; discard peel. Add eggs and whisk to blend; add butter.
Stir over medium-low heat until mixture thickly coats a metal spoopn, about 15 minutes. Scrape into a bowl, cover and chill until cold, at least 1 hour. Stir before using.
Used as filling for Lime Tarts with Coconut Cream