Preheat the oven to 350°F and set a rack in the middle. Toast your English muffins in the preheated oven until they’re lightly golden brown, about 5 minutes. Set aside and let cool slightly.
Poach your eggs. Bring a small saucepan full of water to a rolling boil over high heat. Reduce the heat to medium-low and crack two eggs into a small fine-meshed sieve. Gently lower the sieve into the water and poach for 4 minutes, or until done to your liking.
Make hollandaise sauce. Place 3 egg yolks in a medium saucepan and whisk together with 1 tablespoon of lemon juice, 1 teaspoon of Dijon mustard, and a pinch of cayenne pepper. Place the pan on medium-low heat and whisk constantly until the mixture thickens about 3 minutes.
Take the sauce off the heat and slowly add in ½ cup butter while continuously whisking to combine. Once all of the butter is incorporated, season with salt and pepper.
Place two slices of smoked salmon on each English muffin and top with a poached egg. Drizzle the hollandaise sauce over the eggs, season with salt and pepper to taste, and serve immediately.