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Set up a double boiler by placing a heatproof bowl over a saucepan of simmering water, making sure the bowl doesn’t touch the water.
In the bowl, whisk together the egg yolks, fresh lemon juice, and a pinch of fine sea salt until the mixture is light and frothy.
Slowly stream in the warm melted butter, whisking constantly until the hollandaise thickens enough to coat the back of a spoon.
Keep the hollandaise warm off the heat, resting the bowl over the pan of hot water.
Fill a medium saucepan with about 2 inches of water and bring to a gentle simmer over medium heat.
Add the white wine vinegar to the simmering water.
Crack each large egg into a separate small bowl.
Gently slide the eggs one at a time into the simmering water and poach for 3–4 minutes for a runny yolk.
Use a slotted spoon to lift out the poached eggs and transfer them to a paper towel–lined plate to drain.
Split the English muffins in half and toast until golden brown.
Place each toasted muffin half on a plate and top with smoked salmon slices.
Carefully place a poached egg on top of each salmon-topped muffin half.
Spoon a generous amount of warm hollandaise over each egg.
Season with freshly ground black pepper and garnish with fresh dill or chives, if desired.
Serve immediately.