Monica, we both have PHDs in this area of Vitamin 'G'...
Noto, Sicily--Corado Constanza (as mentioned by MJStedy) slays the nearby, Bourdain-endorsed frontrunner.
Polignano a Mare, Puglia (2 essential shops, ones that were far superior to the competition) Note that Polignano ranks as one of Europe's Gelato Centers.
a) modern shop Bella Blu-their chewy award-winning flavour 'Torta Sorrento' is worth crossing an ocean for.
b) an older more traditional shop, Il Super Mago del Gelo at 22 pza. Garibaldi (some confusion with nearby shop with nearly-identical name); this old family fave is the sole place where one may order 'gelsi neri', a unique mulbery granite ice.
Hope this helps. Enjoy.
Tante belle cose
I am done. The Menu.