Prepare the poaching liquid by filling two large skillets with about 3 inches of water and dividing the distilled vinegar between them.

Bring both skillets to a gentle simmer over medium heat.

Crack an egg into a cup and carefully slide it into the simmering water.

Repeat with the remaining eggs, poaching them for 3 to 5 minutes, turning occasionally with a spoon, until the whites are firm but the yolks are still runny.

Remove the poached eggs with a slotted spoon and transfer them to a kitchen towel to remove excess water.

While the eggs are poaching, melt butter in a large skillet over medium heat.

Add Canadian bacon and cook until heated through, about a minute on each side.

Toast the English muffin halves and divide them among warmed plates.

Top each muffin half with a slice of Canadian bacon and a poached egg.

Spoon hollandaise sauce generously over the eggs and garnish with finely chopped fresh chives or parsley.

Serve immediately.

To make the hollandaise sauce, melt the butter in a medium pan over medium-low heat.

Remove from the heat and let it stand for 5 minutes.

Skim off and discard the white foam from the surface of the butter.

Carefully pour the clear golden butter into a container with a pouring spout, avoiding the milky solids at the bottom of the pan.

Set the clarified butter aside in a warm spot.

Pour water into a medium saucepan to a depth of about 2 inches and bring to a gentle simmer over medium heat.

In a medium heatproof bowl, combine egg yolks and cold water, whisking until light and frothy.

Place the bowl over the simmering water and whisk constantly and vigorously until the yolks thicken and lighten in color, about 3-4 minutes.

If the eggs begin to scramble or cook too quickly, remove the bowl from the heat and whisk to cool.

Remove the eggs from the heat and whisk for 30 seconds to cool slightly.

Remove the saucepan from the heat and set the bowl over the hot water.

Slowly drizzle the warm clarified butter into the eggs while whisking constantly.

Whisk in lemon juice, salt, and pepper to taste.

If the sauce is too thick, add a few drops of warm water to adjust the consistency.

Serve immediately or keep the hollandaise sauce warm in a bowl over warm water for up to 30 minutes.