Use a large saucepan that fits a steaming basket. Put all the steaming broth ingredients; garlic, water, olive oil, oregano, salt and pepper into the pan. Bring the broth to a boil, then cover the pan with a tight fitting lid, turn the heat down and simmer for 1/2 hour (30 minutes).
While the broth is simmering put some water on to boil the pasta.
After simmering the broth, remove the saucepan from the heat. Put the steaming basket, with the chopped broccoli in it into the saucepan. Put the pan on medium heat. When the broth comes to a boil cover with a tight fitting lid. If steam starts escaping, turn the heat down, but keep the broth at a boil. You need to maintain enough steam in the pan to cook the broccoli.
Check broccoli after about 10 minutes to see how tender it is. It usually takes about 15 minutes, but your idea of tender enough, can mean more or less time. If you need to cook more, just put the cover back on and steam some more. Cook for 3 to 5 minutes longer before checking again.
While the broccoli is cooking, boil the pasta. Drain when cooked. If the pasta is done before the broccoli, toss some olive oil into the pasta to keep it from sticking.
When the broccoli is done to your preference, take the steaming basket out of the pan, leaving the broccoli in it and set it aside.
Add the steaming broth (not the broccoli yet) to the cooked pasta and toss in.
Add the cooked broccoli to the pasta. If you want the broccoli florets to be kept in tact, gently fold the broccoli into the rigatoni, If the broccoli is on the tender side will break up pretty easily as you mix it in. The dish tastes just as good if the broccoli brakes up a bit into pasta. maybe even better.