Cut the florets into small pieces and finely chop the remaining stalk, putting it all into a large shallow casserole pan on a medium heat as you go, with 1 tablespoon of olive oil.
Peel, finely slice and add the garlic, along with the chilli flakes.
Drain and tear in the peppers.
Squash and destone the olives, tearing in the flesh.
Cook for 10 minutes, stirring regularly.
Meanwhile, cook the pasta in a pan of boiling salted water according to the packet instructions, then drain, reserving a mugful of starchy cooking water.
Add the pasta to the broccoli pan, grate in most of the Parmesan and toss together, loosening with splashes of reserved cooking water.
Drain and flake in the tuna, season to perfection, toss again, then finely grate over the remaining Parmesan and serve.