Preheat the oven to 350 degrees. Coat a small ramekin with butter.
Add some ham, cheese, and chives to each buttered ramekin.
Crack an egg into each ramekin, being careful not to break the yolk.
Add the milk, remaining ham, cheese, and chives to the top of each ramekin and season them with sea salt, freshly cracked pepper, and cayenne, to taste.
Place onto a baking tray and cook for 5 minutes; Turn the oven to broil and cook for another 4-5 minutes or until the whites are set but the yolk remains soft.
Remove from the oven and serve immediately. Enjoy.