For what it’s worth , San Giuseppe isn’t listed in Rick’s 2019 Florence & Tuscany 18th Edition guidebook. It’s not in the descriptions, nor marked on his map. Where the above Website link shows its location, is just a big blank part of Rick’s “Siena Hotels & Restaurants” map, simply labeling the Onda neighborhood but with no places marked off on Via Giovanni Dupre. Interesting?!?
That guidebook does recommend, under the Old Town Fine Dining heading, Compagnia del Vinattieri, “a good bet for wine lovers, serves Tuscan dishes with a creative touch … romantic meal under graceful brick arches.” Says owner Marco (a different or the same Marco who owns San Giuseppe ???) is happy to take you down to the marvelous wine cellar, and to leave Rick’s guidebook on the table for a complimentary aperitivo or digestivo, but no mention of chocolate cake. They’re open daily 12:30-15:00 & 19:00-23:00, Via delle Terme 79, tel. 0577-236-568, www.vinattieri.net
Either way, I hope this helps. We’re heading to Tuscany in 2 weeks!