Preheat oven to 230°C/450°F (210°C fan-forced).
Boil broccoli in a large pot of salted water for 2 minutes then remove with a slotted spoon and set aside to cool. In the same pot of water (add more water if needed), cook pasta according to packet instructions. (note 1)
Whilst pasta is cooking, heat olive oil in a large, non-stick frypan. Add chicken breasts and spread it out into a single layer, season with salt and pepper. Cook on high heat for about 2 minutes before turning the chicken once and cook for a further 2 minutes. (note 2) Remove chicken and set aside.
In the same pan, add butter, onions and garlic. Fry on medium heat for 3 minutes then stir in flour. Once a thick paste is formed, add milk, stir well until milk thickens then stir in stock. Bring up to a boil then turn the heat off.
The broccoli should be cool enough to touch by now. Cut into small bite-sized florets.
Now, add browned chicken including juices back into the pan along with broccoli, cream, oregano, salt and pepper. Bring up to boil then turn the heat off.
In a large casserole oven dish, add cooked pasta and pour in creamy chicken and broccoli. Mix well with a spatula. It should be quite saucy.
Top with grated mozzarella cheese and parmesan cheese. Bake for 15 minutes or until golden brown, on the middle shelf.
Allow the pasta bake to set for 10 minutes before serving.