Prepare the Welsh rarebit sauce: melt the butter.
Add the grated cheese and the milk.
Stir over low heat until the cheese melts.
Season and adjust consistency with a little extra milk if necessary.
Lay the required number of trimmed toast slices in a shallow fireproof dish and put 2 tomato slices on each piece.
Heat through in a moderate oven (375°F - Gas Mark 4) or under the grill for a few minutes.
Cut the shelled hard-boiled eggs across in half, while still hot and lay one half on each tomato slice.
Pour over the Welsh rarebit sauce.
Garnish with a sprig of parsley.