Combine all the marinade ingredients in a bowl and mix them well. Pour the sauce over the chopped chicken and marinate for at least 30 mins. (Though I strongly recommend marinating it for at least 4 hrs, and if you can afford more time, for overnight for better flavored chicken. However if you are really short of time, 30 mins is OK.)
Preheat a large skillet on medium high heat and once heated add some cooking oil. Put all the vegetables and rice cakes into the skillet and add the meat on top. Cook them on medium high heat for 3-4 mins. Then reduce the heat to medium to medium low and cook further until all is cooked (about 10 - 15 mins). During cooking, stir often to avoid food sticking onto the pan. You can cover with a lid to speed up the cooking process.
** How to Make Dak Galbi, the Restaurant Way, at Home
Typically, dak galbi is cooked and served in a large round cast iron pan at a restaurant. And I personally think it is essential that you eat it this way because it tastes so much better! Trust me! I use this cast iron skillet (12 inch) for my cooking and it's just perfect.
I love cooking dak galbi at the table (over the portable gas burner) so that we can eat it as things get ready. Typically, the cabbage and rice cakes cook the fastest and the sweet potato the last. If you were to wait until everything cooks then somethings could over cook as a result.
Prepare some lettuce, perilla leaves, sliced garlic, ssamjang (spicy dipping sauce) to make a wrap just like you would with other Korean BBQ.
When you are nearly finished the meal (make sure you leave some meat, vegetables and the sauce in the skillet), you can add some (cooked) udon noodles or rice and stir fry them. I typically use 1 cup of steamed rice, some chopped kimchi, a dash of sesame oil and some shredded seasoned seaweed. Some restaurants also crack an egg over the rice but I personally prefer without it. Also, I don't normally add additional sauce to cook the noodles or rice, but if you want you could add some gochujang (about 1 Tbsp) or make extra marinade then add it.