Quarter fill a small saucepan with hot water from a kettle and heat the water to get it simmering.
In a bowl (one that you can fit on top of the small saucepan, and will not touch the simmering water) beat the yogurt, vinegar and egg yolks together well.
Put the bowl over the saucepan of simmering water and stir continuously until thickened, for approximately 12 – 15 minutes.
Remove from the heat and stir in the salt, mustard and pepper to own taste, and set aside.
Grill the turkey bacon and toast the muffins.
In a medium sized pan of simmering water, poach the eggs, being careful to not overdo them. You want the egg yolks to still be slightly runny, not hard.
Place a slice of bacon on top of each toasted muffin, place a poached egg on the bacon and then serve topped with the healthy hollandaise sauce and some freshly grated black pepper.