Fill a deep sided skillet with water. Bring water up to a simmer. Salt the water and add 1 teaspoon white vinegar. (This helps the whites coagulate.)
Crack whole eggs individually into a ladle, deep spoon or small bowl. Drop gently into the water and cook gently 3-4 minutes until the whites are set but the yolk is still soft.
Drain poached eggs onto paper towels and set aside.
Make the Hollandaise Sauce
Bring a medium sized pot of water to a simmer.
While water is coming up to a simmer, whisk butter and egg yolks together in a large, heat-proof bowl to break apart the butter. It will be chunky and this is totally normal!
Place bowl over simmering water and slowly whisk in hot tap water. The heat of the water and the heat from the simmering water will melt the butter. Mixture will be yellow and look liquidy. Also normal!
Continue to whisk for 7-10 minutes or until mixture thickens and reaches 160 degrees F.
Remove from heat and stir in lemon juice and cayenne. Taste and adjust seasonings as you'd like.
Assemble the Eggs Benedicts
Slice english muffins in half and toast. Butter lightly. Top with ham slices and 1 poached egg each. Drizzle with hollandaise sauce and top with black pepper, if desired.