Step 1: Clarify the butter for the Hollandaise Sauce. Gently melt 1/2 cup unsalted butter in a small saucepan over low heat. Skim off any foam and carefully pour the clear yellow fat into a separate bowl, leaving the white milk solids behind.
Step 2: Set up a double boiler for the Hollandaise. Fill a small saucepan with 1-2 inches of water and bring to a gentle simmer. Place a heatproof bowl over the saucepan, ensuring it does not touch the water.
Step 3: Whisk egg yolks and lemon juice in the heatproof bowl until light yellow and slightly thickened.
Step 4: Cook the yolk mixture over the simmering water, whisking continuously, for 3-5 minutes until pale, foamy, and ribbon-like. Do not stop whisking to prevent scrambling.
Step 5: Remove from heat and slowly drizzle the warm clarified butter into the egg yolk mixture in a thin, steady stream while whisking vigorously until the sauce thickens and emulsifies. Season with salt, cayenne pepper, and adjust lemon juice to taste.
Step 6: Prepare the poaching water. Fill a large, deep skillet or pot with 3-4 inches of water. Add 1-2 tablespoons of white vinegar and a pinch of salt. Bring to a bare simmer.
Step 7: Crack each egg into individual small bowls. Gently create a swirl in the simmering water with a spoon, then carefully slide each egg into the center of the swirl.
Step 8: Poach eggs for 3-4 minutes for a runny yolk. Cook in batches if needed to avoid overcrowding the pan.
Step 9: Remove poached eggs with a slotted spoon and gently blot excess water with a paper towel. Set aside.
Step 10: Toast the English muffins until golden brown and slightly crispy.
Step 11: Gently fry or warm the Canadian bacon slices in a non-stick skillet over medium heat until lightly browned and heated through.
Step 12: Assemble the Eggs Benedict. Place a toasted English muffin half on each plate, top with a slice of warm Canadian bacon, then a poached egg.
Step 13: Generously spoon the warm Hollandaise sauce over each egg.
Step 14: Garnish with fresh chopped chives or paprika, if desired, and serve immediately.