Start by bringing a pot of water to a rolling boil. Carefully lower the eggs into the boiling water and set a timer for 7½ minutes. Prepare an ice bath with cold water and ice.

While the eggs cool, combine gochujang paste, mayonnaise, and sesame oil in a bowl. Add brown sugar if desired, and whisk until smooth.

Peel the cooled eggs under running water, then mash them in a bowl. Fold in the gochujang mayo; season with salt and pepper to taste.

Toast the sourdough bread until golden brown. Spread butter on the toast while warm.

Spoon the egg salad onto the toast, add kimchi, and garnish with sesame seeds and chives.