Korean Street Toast

Ingredients (14)

• + ⅓ cup julienned carrot add to pantry
• + 1 cup thinly sliced green cabbage add to pantry
• + 1 stalk green onion, thinly sliced add to pantry
• ✓ ¼ teaspoon ground black pepper
• + 1 pinch cayenne pepper add to pantry
• ✓ ½ teaspoon kosher salt, or to taste
• + 2 large eggs add to pantry
• + 3 tablespoons salted butter, divided add to pantry
• + 2 thick slices white bread add to pantry
• + ½ teaspoon white sugar, or to taste add to pantry
• + 2 thin slices smoked ham add to pantry
• + 1 slice mild Cheddar cheese add to pantry
• + 1 tablespoon ketchup, or to taste add to pantry
• ✓ 1 tablespoon mayonnaise, or to taste