The Institute of Korean Food has a really good English language site. They offer cooking classes for tourists as well as an academic programs for aspiring chefs and various continuing education classes for professional chefs to improve their skills.
The Food and Culture Korea Co. also offers a wide variety of classes from single dish classes for tourists and ex-pats to academic programs for aspiring chefs and restaurant managers. As I scanned their website, I found a picture of my favorite Korean drama actor Bae Yong Joon. Mr. Bae owns several restaurants (two in Korea, two in Japan). From the age of the picture, it seems he visited them around the time he began his second career as a restaurateur. Here's additional information from the Korea Herald article about the three cooking academies including contact information and directions:
Institute of Traditional Korean Food
Classes last three hours and are taught in English, Japanese and Chinese. Prices range from 50,000 won to 70,000 won per person. Only groups of 20 or more can arrange for a class. Applicants can pick from a range of rice cake, kimchi and traditional Korean dishes. Reservations should be made at least a week in advance.
Free cooking classes for Japanese tourists are held every Saturday through November.
The institute is located near Jongno 3-ga Subway Station Line 3, Exit 7. After exiting the subway station, walk straight, past two stoplights. It will be on your left.
For more information call (02) 741-5477 or visit www.kfr.or.kr
Food and Culture Korea Co.
Classes are taught in English and Japanese. Prices range from 25,000 won to 50,000 won per dish. Only groups of two or more can take a class. To get there go to Gyeongbok Palace Subway Station Line 3, Exit 2. Walk straight for approximately 500 meters. For more information call (02) 720-6704, visit www.fnckorea.com or send an e-mail to email@example.com
Edited January 23, 2011: Han's Cooking Academy closed their doors in 2010, and their niche is held now by O’ngo Food Communications. O’ngo Food Communications offers cooking classes as well as market tours to introduce students to the basic ingredients of Korean cuisine.