Toast your bread and set aside.
Put a nonstick pan on medium heat and add the oil. Let the oil come to temperature.
Roughly shape the kimchi into "circles" on the pan, making two areas that you can crack the eggs into. The pan should be hot enough that the kimchi sizzles when it hits.
Crack the eggs into the center of the kimchi "circles," season with just a pinch of kosher salt. Cover and cook for 2-3 minutes or until the whites are fully set.
Scoop one egg onto each piece of toast. Drizzle with the chili oil and add extra kimichi as you prefer. Scatter with the basil or mint and finish with a few cracks of black pepper. Eat immediately!