Remove the egg poacher and fill the pan with water. Bring to a boil.
Lightly grease the egg poacher and crack the eggs into it.
Reduce the heat under the pan, then place the egg poacher in the water and cover the pan.
Cook for about 2 minutes for runny eggs.
In the meantime, toast the bagels.
Place a slice of ham on each bagel half.
Place the poached eggs on top, then drizzle with hollandaise sauce and garnish with chopped parsley (optional).
Serve immediately.
Hollandaise sauce:
In a small saucepan over medium heat, reduce the vinegar, water, and salt until about 3 tablespoons of liquid remain.
Remove from heat.
Return to low heat. Place the egg yolks in the saucepan with the reduced vinegar and beat constantly until the mixture is foamy and slightly thickened. Be careful not to scramble the eggs!
If the eggs start to cook too quickly, remove them from the heat and beat them vigorously to cool them down before continuing.
Using a whisk, start incorporating the butter a piece at a time.
Once all the butter has been incorporated, whisk in the lemon juice and white pepper.
Use immediately.