Preheat the oven to 200°F (95°C). Place two clean, oven-safe plates inside. These will be used to keep the toasted muffins and poached eggs warm as you work.

Toast all four English muffin halves until golden. Transfer them to one of the warm plates in the oven.

Crack 1–2 eggs at a time into a small bowl of cool water with a small splash of vinegar. Let the eggs sit for 2–4 minutes. This lightly firms the whites and helps prevent wispy edges when poaching.

Bring a saucepan of water to a bare simmer—tiny bubbles clinging to the bottom, but no rolling boil. Add 1 teaspoon of vinegar to the water.

Gently lift each egg from the pre-soak and lower it into the simmering water. Poach for 3–4 minutes, until the whites are set and the yolks are still soft. Lift out with a slotted spoon, drain briefly on a paper towel, then place the eggs on the second warm plate in the oven.

Arrange smoked salmon over each toasted muffin half. Top with a warm poached egg and spoon hollandaise generously over each.

Scatter with capers, chopped dill, and freshly ground black pepper. Serve immediately.