Make the hollandaise sauce: In a blender, place the egg yolks, lemon juice, mustard, salt, and cayenne. Blend for 5 to 15 seconds, or until the mixture is frothy.

Place the butter in a small pot over medium-low heat. Cook, stirring, until melted. Transfer the melted butter to a glass liquid measuring cup so that it’s easy to pour. With the blender running on low, slowly pour in the hot butter, blending until the sauce is emulsified. The sauce should have a thick but pourable consistency. If it’s too thick, blend in hot water, 1 tablespoon at a time, to loosen it. Set aside while you poach the eggs.

Poach the eggs. Crack four of the eggs into four separate small bowls or ramekins. Bring a medium pot of water to a gentle boil. Add the vinegar and stir the water so that it moves in a circular motion. Gently drop the eggs into the water, give the water another gentle stir, and cook for 3 minutes and 30 seconds to 4 minutes. Use a slotted spoon to scoop the eggs out of the water and test for doneness. Set aside and repeat with the remaining eggs.

Assemble the eggs Benedict: Slice the English muffins in half and lightly toast.

Top each half with a tomato slice and a poached egg. Season the egg with salt and pepper, then drizzle generously with the hollandaise sauce. Garnish with fresh chives and dill and serve immediately.