1.In a bowl, whisk together the ketchup and remaining ingredients except for the oil. Once combined, slowly drizzle in the oil while whisking continuously to incorporate. Set aside until ready to use.
2.Bring a saucepan of water to the boil and add 2 tbsp white wine vinegar. Break the eggs into 4 separate coffee cups or ramekins.
3.Swirl the vinegared water briskly to form a vortex and slide in an egg. Let it curl around and Cook for 2-3 mins, then remove with a slotted spoon. Repeat with remaining eggs.
4.Split the buns in half and toast them
5.Spread a drop of sauce on each half of the buns Top with a scrunched up piece of ham followed by a poached egg. Spoon over the sauce to top and garnish with chopped chives.