Fill a large saucepan with 3 or 4 inches of water.  The pan should be large enough to comfortably poach 4 eggs without crowding them.   Heat the water on medium-high heat until small bubbles appear on the sides and bottom of the saucepan. Reduce the heat to low and keep at a simmer.  

In a mini-food processor or a blender, add the egg yolks, mustard, lemon juice, process for 30 seconds.

In a small saucepan set over medium heat, add the butter and heat slowly until it is melted and just begins to foam. Transfer the melted butter to a small pitcher or pourable container.

With the processor running, slowly, drizzle the melted butter through the lid opening into the egg mixture. Continue processing and drizzling until all the butter has been incorporated. About 3 minutes. The egg mixture will begin to emulsify and thicken. If it becomes thicker than you like, thin with a tablespoon or more of hot water (or lemon juice) to the desired consistency. Stop the motor and add salt and pepper to taste and whiz again for a second or two.

Transfer the hollandaise sauce into a small pitcher, set the pitcher in a dish of hot tap water to keep warm. 

Break the eggs, one at a time into a fine-mesh strainer, swirl the egg around allowing the watery liquid to drain off. Transfer the eggs into individual small custard dishes.  Tip each egg into the simmering water and poach for 3 to 4 minutes or until desired doneness. 

Toast, butter and plate the English muffins. Add a tablespoon of hollandaise sauce to each half of muffin. Add 2 slices of smoked salmon. 

When the eggs are cooked, remove them one at a time with a slotted spoon, blot the underside of the spoon to remove the excess water and slide the egg onto the smoked salmon. 

Spoon another 1 tablespoons of the warm hollandaise sauce over each egg, sprinkle with snipped chives and serve immediately.