Pat the chicken breast dry, then cut it into small, even pieces so it cooks quickly and evenly.
Finely chop the onion and mince the garlic. Having everything prepped makes the cooking process smooth and easy.
Add the onion to a skillet over low heat and cook until soft and lightly golden, stirring occasionally.
Add the chicken pieces to the skillet, season with salt and black pepper, and cook over medium heat until the chicken is mostly cooked through.
Rinse the broccoli and cut it into bite-sized florets so they cook evenly and stay tender.
Add the bay leaves and broccoli to the skillet, along with the garlic and oregano. Stir gently so the broccoli is coated in the sauce and seasonings.
Pour in the heavy cream and stir until everything is evenly combined and the sauce begins to come together.
Let the mixture simmer for about 8 minutes, stirring occasionally, until the broccoli is tender and the sauce has thickened slightly.
Remove the bay leaves, sprinkle in the cheese, and stir until melted and creamy. Turn off the heat and serve right away.