Prepare the Hollandaise sauce by whisking egg yolks and lemon juice in a heatproof bowl set over a pan of simmering water, ensuring the bowl does not touch the water.

Slowly drizzle in the melted butter while whisking constantly until the sauce thickens and becomes creamy, about 3-5 minutes.

Remove the sauce from heat, stir in the fresh dill, season with salt and pepper, and cover to keep warm.

Fill a large saucepan with water, add vinegar, and bring to a gentle simmer over medium heat.

Crack each egg into a small ramekin first, then slide them gently into the simmering water one by one.

Poach the eggs for 3-4 minutes until the whites are fully set but the yolks remain runny, then remove carefully with a slotted spoon.

While the eggs cook, toast the English muffin halves in a toaster or under a broiler until golden brown and crisp.

To assemble, place two toasted muffin halves on each plate and top each with a generous slice of smoked salmon.

Place a poached egg carefully on top of the salmon.

Spoon the warm dill Hollandaise sauce generously over the eggs and garnish with extra dill or chives before serving immediately.