Preparation

• Position a rack in the center of the oven, put a baking sheet on it, and heat the oven to 200°F.
• In a medium bowl, whisk together the flour, baking powder, baking soda, and 1/2 tsp. salt. In another medium bowl, whisk together the buttermilk, 1 egg, the 3 Tbs. chopped cilantro, the lime zest, and chile, if using. Gently whisk the wet ingredients into the dry until barely combined. Stir in the butter. The batter will be very thick.
• Let the batter rest while you heat a griddle or nonstick skillet over medium heat. Lightly oil the griddle. Working in batches, pour 2 Tbs. of the batter onto the griddle for each pancake, spacing them about 1 inch apart and gently spreading them with the back of a spoon or silicone spatula to a 3-1/2-inch diameter. Let cook undisturbed until bubbles rise to the surface and the edges look dry, 1 to 2 minutes. Check the underside of each pancake to make sure it’s nicely browned, then flip. Cook until the second side is nicely browned, about 1 minute more. Transfer the pancakes to one side of the baking sheet and keep warm in the oven while you repeat with the remaining batter.
• Raise the heat under the griddle to medium high. Fry the kimchi, pressing down on it with a spatula and flipping halfway through cooking, until hot and lightly browned, about 4 minutes total. Transfer the kimchi to the baking sheet with the pancakes. Wipe off the griddle, lightly oil, and cook the remaining eggs to your liking (for example, 6 sunny-side-up eggs). Serve the pancakes with a fried egg. Garnish with the sliced cilantro, and serve with the mayo on the side, if using.