There are many steps to this dish but many pieces can be going at the same time. You can find the Gochujang, the Korean BBQ sauce and the Korean Chile flakes in an Asian market or some Asian sections of larger markets. The bun, which is a traditional Korean street food usually has an egg baked inside of the batter as it cooks, but I'm putting the patty and Kim-Chi in the bun instead with a spicy aioli. The flavors are tangy and spicy but not too hot so you'll be able to enjoy the flavors of the meat and cabbage. It's a twist on the classic burger adding an international flair. Enjoy.
For the buns: Pre heat an oven to 425 deg. F. Whisk together the dry ingredients in a large bowl. Add the wet ingredients and whisk until smooth. Fold in the cilantro.
Grease a six compartment muffin tin with butter or spray and divide the batter between the compartments. Sprinkle the basil and grated cheese over the top of each compartment.
Put the muffin tin in the oven, lower the heat to 400, and bake for 20 to 25 minutes, or until a toothpick inserted into the middle comes out clean. Remove from the oven and remove the buns and set aside to cool while everything else is being prepared.
For the sliders: In a small bowl mix together all of the slider seasonings.
In a medium sized bowl break up the meat, add the seasoning mixture and combine. Don't over mix. Separate into 6 patties, about 2-1/2" in diameter. I use a 2-1/2" cookie mold the keep the size uniform and press down to make them a little larger. If you're not going to cook them right away, set in the refrigerator until ready to cook. Remove from the refrigerator about 15 minutes before you're ready to prepare them.
Using a cast iron pan or non-stick frying pan heated to medium high, put on the patties and cook on each side for 3 to 3-1/2 minutes to your desired doneness. At 3-1/2 minutes they should be medium rare. But watch carefully. Remove from the heat and assemble the sliders.
For the Kim Chi: Put the water up to boil in a large pot.
Wash the cabbage and shake out the water. Cut off the bottom end of the cabbage and cut the bottom 5" leaving the top, leafy ends for another use. Slice the cabbage lengthwise into medium strips and then crosswise. Place in a large bowl with the shredded carrots.
When the water starts to boil, add the salt and continue to boil until the salt is dissolved. When dissolved, turn off the water and let cool of 5 to 10 minutes.
After the water has cooled, pour over the cabbage and carrots and let it set for 10 minutes, mixing it around occasionally. During this time make the seasoning mixture. After 10 minutes drain and rinse the cabbage and carrots. Return to the bowl
In a blender add all of the Kimchi seasonings except for the sliced chili and the sesame seeds and blend until smooth. Pour over the cabbage and carrots and combine thoroughly. If you're mixing by hand put on rubber gloves. Top with the sesame seeds and sliced chili and set aside.
For the Aioli: Mix together the mayo and Gochujang and refrigerate until ready to assemble the burgers.
Assembling the sliders: Slice each bun in half and spread about 1 teaspoon of the aoili on the bottom half of each bun. More if you want it spicier. Place a patty on each of the bun bottoms, top with some of the kim-chi, cover with the bun tops and serve.