For the hollandaise sauce, place the white wine, white wine vinegar, black peppercorns and sliced shallots into a heavy-based pan (not aluminium) over a high heat.
Bring the contents to the boil and reduce the liquid in the pan to half its original volume. This will take about 15 minutes. (This will make more reduction than you'll need for this recipe. You can store the reduction in the fridge for up to a month or so, for future use.)
While the white wine and vinegar mixture is reducing, place the butter in a small heavy-bottomed pan and melt over a low heat.
When the butter has melted, using a spoon, skim the white foamy bits (milk solids) from the surface of the butter. Remove the clarified butter from the heat and allow to cool to blood temperature.
Place a clean glass bowl over a pan of simmering water. The water should not touch the bottom of the bowl.
Place the egg yolks in the bowl set over the pan of water and whisk. Add about one tablespoon of the vinegar and shallot reduction. Whisk the egg yolk mixture vigorously and constantly for about five minutes, until the mixture turns foamy and then thickens.
The mixture is ready when the mixture falls from the whisk in strands that rest for a second or two on the surface before settling back into the egg mixture.
Remove the egg mixture from the heat. Pour a small amount of the blood-temperature clarified butter into the egg mixture and whisk vigorously until the butter is completely incorporated. Gradually add the rest of the clarified butter to the egg mixture, bit by bit, whisking in all the butter until a smooth, thick, emulsified sauce is formed.
If you work slowly and if the ingredients are all of the same temperature, the sauce shouldn't split. If it splits, it's either too hot or too cold. If it's too cold (feels cool to the touch), warm the butter up and whisk in the warmed butter, which should re-emulsify the sauce. If it's too hot (feels very warm to the touch), drop an ice cube into the sauce and whisk again to re-emulsify. Once properly emulsified, the sauce will remain stable, giving you time to prepare the rest of the dish.
To poach the eggs, fill a tall pan with water. Bring to the boil and add three tablespoons of white wine vinegar per pint of water. Make a 'whirlpool' in the pan by swirling a slotted spoon around the outside edge of the pan. Carefully crack the eggs into the pan, in the centre of the whirlpool.
Poach the eggs until the whites are firm but there's still movement in the yolk - they'll feel firm to the touch when ready.
To serve, place half a muffin on each plate. Top with a slice of ham, the other muffin half and another slice of ham. Carefully remove the poached eggs from the pan with a slotted spoon and place on top of the ham. Spoon the hollandaise sauce on top and around the muffins and serve immediately.