In a large saucepan, bring 6 cups water to a boil over high heat.
Add the vinegar and lower the heat until it is no longer at a rolling boil.
Crack an egg into a small cup, dish, or wineglass.
Holding it near the surface of the water, gently slide the egg into the hot water.
Repeat with the remaining eggs.
Cover the saucepan and allow the eggs to cook for exactly 6 minutes.
Remove each egg carefully with a slotted spoon and drain on a paper towel.
Toast the English muffins.
Cook the bacon until cooked through, 2 to 3 minutes on each side.
Place a slice of bacon on each toasted English muffin half.
In the same skillet, melt 1 tablespoon of the butter over medium heat.
Add the garlic and cook until fragrant, about 30 seconds.
Add the asparagus, cover the pan, and cook, tossing occasionally, until tender, about 8 minutes.
In a medium bowl, whisk the remaining 1 tablespoon butter with the yogurt, egg yolks, lemon juice, mustard, cayenne, and salt.
Transfer the mixture to the top of a double boiler, set it over simmering water, and heat it, whisking continuously until the mixture thickens, about 5 minutes.
Immediately remove from the heat.
To assemble the dish, place 3 asparagus spears over the bacon on each muffin half, and top with 1 poached egg and 2 tablespoons of the hollandaise sauce.