Melt the butter in a small saucepan over medium low heat.
In a medium bowl, add the egg yolks, dijon mustard, and 2 teaspoons of water. Blend with an immersion blender, gradually adding the melted butter in a steady stream. Add the lemon, cayenne and salt to season, and blend until fully incorporated and fluidious. If the sauce is too thick, add a little more water. Cover with plastic wrap and set aside until ready to use.
Preheat the oven to 400 degrees F. Place bacon on a baking sheet and bake for 20 minutes.
Bring a medium pot of water to a low simmer and add the vinegar. Crack one egg into a small bowl. With a spoon, stir the water until it spins in a clockwise direction to create a vortex. Gently lower cracked egg into the spinning water and cook for 3-4 minutes until whites are just set. Remove with a slotted spoon and drain on a paper-towel lined plate. Repeat with the remaining eggs.
To assemble: Layer a slice of tomato and bacon on each of four halves of english muffin. Place one poached egg on top and pour over with hollandaise sauce. Garnish with chives.