This venue is a classic among locals (it is traditional to go there and eat ensaimada with hot cocoa after New Year's Eve). Pastries, both sweet and salty, are excellent and reasonably priced, if not exactly diet-friendly. For the non-initiated in local cuisine, remember to leave all ideas of French confectionery at the door: everything is solid, filling and made with either saïm (refined pork lard) or olive oil, as is customary in Mallorca.
If you are looking for something lighter, order "coca de quarto", a biscuit made of ultrafine wheat flour and egg white (no lard) or for the curious, "coca de patata" (made with potato flour), a more peasant-like concoction from a time when fine wheat flour and white sugar could only be afforded by a small élite of landowners and the clergy.
Ice cream is home-made and excellent, served in small glasses filled to the brim; try the almond ice-cream, a house special.
Also note the decoration, which reflects traditional Mallorcan style with hand-made glass chandeliers (not unlike Murano glass chandeliers, though they are also a local tradition), dark woods, old-fashioned chairs and marble-top tables. Waiters are similary old-fashioned but very nice, and I would be surprised if they spoke anything foreign (you can always point, pastries are on display).
No frills and no minimalism for a slightly nineteenth-century atmosphere; you will find no tourists here.
By the way, on busy hours - afternoons and evenings - there is almost always a long queue, so better head there in the morning when locals are working (on weekdays) or sleeping (on weekends). And remember that there is a "new" Ca'n Joan de S'Aigo at Baró de Santa Maria del Sepulcre, 5 (it's been there for years but that is considered new by Palma's standards); you will probably walk very close if you go shopping at Jaime III street.