Well, it has basically been figured out, and fairly well documented.
Some of the staright answers are only a handful of posts before yours, so look back a page. :)
Basically, you partner up with someone and talk to an npc after some events, and you get a food item as you reward.
Yoten wrote:
For the next part, form a party of two people and have each person get their fortune from Emila (if they haven't already). Since the title you receive is the one of the person you're most compatible with, have your partner change his title to that one. Once both people have their partner's compatible title, talk to one of the NPCs in the various nations to receive two food items.
Port San d'Oria -- G-7 -- Perdiouvilet
Port Bastok -- J-7 -- Brita
Windurst Waters (north) -- E-10 -- Dabido-Sorobido
Checking the Luck Rune and talking to the NPCs... do these two things (the order doesn't matter) and you can receive another fortune. You can do this once per Vana'Diel day.
The food you can receive is listed below. The rewards have four levels, depending on your compatibility with your partner.
I. "Best Partner"
Sub-zero Gelato, Vermillion Jelly, Rolanberry Pie +1
II. ???
Optical Soup, Boiled Cockatrice, Shallops Tropicale, Sophic Stew, Marbled Steak
III. ???
IV. ???
Shogun Rice Ball, Timbre Timbers Salad