Fill a saucepan with about 3 inches of water and bring to a gentle simmer. Add the white vinegar to a shallow bowl for poaching.
Crack the whole egg into the simmering water and poach for about 3 minutes until the white is set but the yolk is still runny. Remove with a slotted spoon and drain on a paper towel.
In a heatproof bowl set over a pot of simmering water (double boiler), whisk together the 3 egg yolks and lemon juice until thickened and pale.
Slowly drizzle in the 1/2 cup melted butter while continuously whisking until the sauce is smooth and creamy. Stir in the pinch of cayenne, and season with salt and black pepper to taste. Keep warm.
In a skillet, melt the 1 tbsp butter over medium heat and cook the back bacon slices until crisp and browned on both sides. Remove and set aside.
Split and toast the English muffin halves until golden.
Assemble the Eggs Benedict by placing the toasted muffin halves on a plate, topping each with a slice of back bacon, then the poached egg.
Spoon the warm hollandaise sauce generously over each poached egg.
Garnish with freshly chopped chives and a sprinkle of black pepper. Serve immediately.