Pat the chicken breast dry, then cut it into small, even bite-size pieces.
Finely chop the onion and mince the garlic. Rinse the broccoli and cut it into bite-size florets.
Add the onion to a large skillet over medium heat and cook until softened.
Add the chicken, season with salt and black pepper, and cook until the pieces are lightly golden on the outside.
Add the broccoli and bay leaves. Season with a little more salt and black pepper, then stir in the garlic and oregano.
Pour in the heavy cream and stir gently until everything is evenly combined.
Reduce the heat slightly and simmer gently for about 8 minutes, stirring occasionally, until the broccoli is tender but still slightly firm and the sauce has thickened.
Remove the bay leaves. Reduce the heat to low, add the shredded cheese, and stir until completely melted and the sauce is smooth and creamy.
Turn off the heat and serve immediately while the sauce is hot and creamy.