Whisk flour, water, sugar, salt, and pepper in a large bowl. Make sure there are no lumps.
Add green onion and kimchi, into the batter. It's ok if your kimchi is juicy. Mix well with a spoon.
Heat a 12-inch, well seasoned, cast iron skillet on medium high heat. When the pan is hot, add 2 Tbsp neutral oil (I used grapeseed oil). The oil should thin on contact and smoke slightly.
Add 1 cup of kimchi pancake batter. Use a spoon to spread the batter as thin as possible, all the way to the edges. When the bottom is crispy with browned spots, flip to the other side and finish cooking, about 3-4 minutes on each side.
When the second side is done, about another 3-4 minutes, flip back to the first side and cook for an additional 1 minute. This will ensure the crispiest pancake.
While the pancake sizzles away, make the dipping sauce. (This is optional.) Combine all ingredients in a small bowl and set aside.
Remove from pan. Slice into pieces with a pizza cutter or knife. Garnish (if desired) with green onion or cilantro and a sprinkle of sesame seeds. Serve with dipping sauce and eat immediately.