broccoli "stuff"

this is a wrong version of two different things, but it's quite nice!

enough for 4 people, I reckon.

A large chopped onion,
a "head" of broccoli (if that's the word),
4 med chopped button mushrooms,
100g cheese of your choice (NOT emmental(sic), it's rubbish),
250ml cream (18% stuff for cooking),
and egg yolk,
pinch of salt, pepper

serve with pasta or boiled potatoes; I've done both.

Now, I'd never actually cooked broccoli before - hope it wasn't one of those 1000 things you're supposed to have done before you're thirty (like sky-dive with Paris Hilton, eat a Ferrari and orchestrate a coup in Latin America etc etc etc). And I didn't ask for any advice.
So this is what I did: cut the small heads off the big daddy head, and boiled them for 8 minutes. I chose that number arbitrarily.
At the same time, I fried the chopped onion in butter over a low-ish heat for 5 mins, then added the mushrooms.
Drained the broccoli, and left it to think about its future for a while.

As far as timing goes, I wanted the potatoes to be ready at the same time, so with ten minutes to go (out of 15-20 for boiling potatoes), I added the cream to the onion etc, and heated it quickly, then lowered the heat again. Added salt and pepper. Not enough salt for anyone else's tastes, mind you.
Oh, you will have grated your cheese!
...which I stirred into the cream bit by bit until it all started to thicken. Once that was done, the egg yolk was next; stirred in as quickly as was possible without without making a big mess. Heat was lowered as low as low could go, and the broccoli dumped in and stirred about a bit.
I left it, again, while the pasta or potatoes were drained, and put on plates, then the broccoli mixture on top of or next to the carbohydrates.

That was that. It was good, according to the two reviews it has had so far.