In a medium saucepan, melt the butter over low heat. In a mixing bowl, whisk together egg yolks, lemon juice, and a pinch of salt. Gradually add the melted butter to the egg mixture while whisking continuously until thickened. Set aside but keep warm.
Fill a medium saucepan with water and add the white wine vinegar. Bring to a gentle simmer. Crack each egg into a small bowl and gently slide them into the simmering water. Poach for about 3-4 minutes until the whites are firm but the yolks are still runny. Use a slotted spoon to carefully remove the eggs and drain on a paper towel.
While the eggs are poaching, toast the English muffins until golden brown.
On each toasted English muffin half, layer slices of avocado and a portion of smoked salmon. Place a poached egg on top of each.
Generously drizzle the warm Hollandaise sauce over each poached egg.
Season with salt and freshly ground black pepper, and garnish with fresh dill or chives if desired.