Set up a bain-marie by placing a heatproof bowl over a saucepan of simmering water, ensuring the bowl doesn’t touch the water.
In the bowl, whisk the egg yolks with the fresh lemon juice and fine sea salt until light and frothy.
Slowly drizzle in the warm melted unsalted butter while continuously whisking until the sauce thickens enough to coat the back of a spoon.
Keep the hollandaise sauce warm over the bain-marie, off the heat.
Fill a medium saucepan two-thirds full of water and bring to a gentle simmer.
Add the white wine vinegar to the simmering water.
Crack each large fresh egg into a separate small ramekin.
Gently slide one egg at a time into the simmering water and poach for 3–4 minutes for a runny yolk.
Use a slotted spoon to lift each poached egg out and drain on kitchen paper.
Slice the English muffins in half and toast until golden brown.
Place each toasted muffin half on a plate and top with good quality smoked salmon slices.
Carefully place a poached egg on top of each salmon-topped muffin half.
Spoon a generous amount of warm hollandaise sauce over each egg.
Garnish with fresh dill or chives if using, and season with freshly ground black pepper.
Serve immediately.