For the hollandaise: In a small saucepan, melt the butter over low heat. Once melted, pour into a pitcher and set aside to cool slightly. In another saucepan, heat water to a simmer and place a glass bowl on top, creating a double boiler. (Make sure the bottom of the bowl isn't in contact with the water.) Place the egg yolks into the warmed glass bowl. Whisk continuously, moving the bowl on and off the heat so the temperature remains consistent. The eggs will get pale and double in volume while they’re being whisked. It’s important the yolks and butter are the same temperature for proper emulsification, so wait for the butter to cool before adding.
Cook the Canadian bacon: In a skillet, heat the butter over medium to high heat until foamy. Add the bacon and lay a plate on top for even browning, about 45 seconds. Flip and brown the other side; then remove from heat.
Continue making the hollandaise: Briefly re-whisk the yolks over the double boiler to smooth out the texture. After ensuring the melted butter from Step 1 is the same temperature as the egg yolks, slowly drizzle half the butter into yolks, a little at a time, whisking continuously to emulsify. Once half the butter has been incorporated, add vinegar and salt, thinning with warm water as needed. Follow with lemon juice. Continue to whisk in the rest of the butter, stopping when there’s nothing left but the white butter solids; reserve and set aside the solids. Store hollandaise in a thermos; the hollandaise should stay warm for up to an hour. (Makes about ¼ cup.)
Poach the eggs: Fill a medium saucepan with 3 inches of water and bring to a simmer. Add white vinegar and salt; taste the water to make sure it's sufficiently seasoned. Crack the eggs into ramekins. Using a spoon, stir the water in a clockwise motion. Drop the eggs in one at a time and let them cook until the whites are no longer jiggly to the touch, about 1½ minutes. Using a slotted spoon, remove to a plate, top with butter, and set aside. (Always poach one extra egg, just in case.)
Assemble the dish: Brush English muffins with leftover butter solids and toast in skillet until crispy. Add two slices of Canadian bacon to each muffin, followed by a poached egg, a dot of butter, and a few tablespoons of hollandaise. Garnish with chives and pepper and serve.