The term polonaise [‘Polish-style’] denotes the use of parsley in a dish; in this case, the garnish also includes sieved hard-boiled eggs and breadcrumbs.
Shell the eggs and separate the whites from the yolks then pass the whites through a coarse sieve followed by the yolks. Stir through the parsley.
Cook the broccoli in plenty of boiling, well-salted water for 1-2 minutes then drain well. Arrange the broccoli in a warm, buttered gratin dish and scatter with the egg and parsley mixture.