Eat at Hyakugawa in Rakunai to begin the friendship gauge.
After you get the gauge above half full, Ryoma notices 2 of the brothers having an argument over what's better - Chinese food or Western-style food. Then all 3 brothers end up arguing over what style of food they are going to serve here - Japanese style, Western style or Chinese style. Then they decide they'll let Ryoma decide what style they should go with! So they're going to have a cooking competition - all 3 will make a different dish (Japanese, Chinese and Western) and Ryoma will decide which is the best. After that, Ryoma leaves.
You can go back inside and eat again to build up the gauge.
Then the next time you go inside, their meals (for their competition) are ready for Ryoma to try. Select the TOP OPTION to try the food.
The first brother serves Ryoma a Japanese style meal. Next, the second brother serves Ryoma a Chinese style meal. Finally, the third brother serves Ryoma a Western style meal. After each meal, Ryoma (thinking to himself) heaps lots of praise on the dish and how delicious it is. Now you have to choose... Choose the top option for Japanese style, middle for Chinese and bottom for Western. It makes no difference what you choose or what order you choose them in. In the end, Ryoma says he can't decide which is the best because they were all so good!
Next it goes into a Japanese play on words... This is not making it into the English version (if one gets released), that's for sure. When Ryoma can't decide which is best, he says "Wakaran" ("I don't know" as in "I don't know which is best"). Eventually, the older brother realises something and merges the words for the 3 styles of cooking into one - Japanese cooking ("Washoku"), Chinese cooking ("Chuka") and the Western cooking, which used a style from Holland (the abbreviation for Holland in Japanese is "ran") - which leads to "Wakaran" (it's actually a pretty good play on words, lol). So now they are going to call themselves "Wakaran Cooking".
They thank Ryoma and reward him with a Broken Compass. After that, the friendship gauge is maxed out.