Cut any tough parts from the broccoli and cook the trimmed stems in boiling, lightly salted water for 3-4 mins. Drain and keep warm in a low oven along with 2 plates.
Next, make the sauce. Gently melt the butter in a small pan over a low heat. Meanwhile, crack the eggs into the jug of a blender and add the mustard, lemon juice and seasoning with a dash of chilli or Tabasco. Turn up the heat until the butter begins to bubble. With the motor running, pour it, in a thin stream, into the blender through the hole in the lid. Continue to run the motor for about 30 secs after all the butter is in to make sure the sauce is fully mixed. Set aside.
Heat a large pan of water. Crack an egg into a teacup and, once the water is simmering, tip the egg into the pan, then repeat with the 3 remaining eggs. Cook for 3 mins, then take them out in the order you put them in.
Meanwhile, toast the bread and keep warm. To serve, lay a slice of toast on each warm plate. Lift the eggs from the water using a slotted spoon, drain them well and place 2 eggs on each slice of toast. Serve the broccoli alongside and spoon some hollandaise sauce over, putting the rest in a small bowl. Serve at once.