Mix ¼ tsp vinegar and the yolk from the separated egg in a small bowl. Blend the egg yolk using a stick blender while slowly drizzling in the melted spread while it's still warm. Blend the sauce for another minute or so, until thick.
Bring a pan of water to the boil over a high heat, then reduce to a low simmer. Add the remaining vinegar and gently break the eggs into the water. Cook for 1½ minutes. Remove with a slotted spoon on to kitchen paper.
Meanwhile, toast the muffin halves. Top with the parma ham and poached eggs. Pour over the hollandaise sauce and serve sprinkled with chives.