Preheat your oven to 375°F (190°C).
In a large pot of boiling water, blanch the broccoli florets for about 2 minutes. Drain and set aside.
In a medium bowl, combine the mayonnaise, sour cream, minced garlic, dried oregano, dried basil, grated Parmesan cheese, salt, and pepper. Mix well.
Place the chicken breasts in a baking dish. Season them with salt and pepper.
Spread the mayonnaise mixture evenly over the chicken breasts, making sure to coat them completely.
Arrange the blanched broccoli florets around the chicken breasts.
Sprinkle the shredded cheddar cheese over the chicken and broccoli.
Cover the baking dish with foil and bake for 25 minutes.
Remove the foil and continue baking for an additional 15 minutes, or until the chicken is cooked through and the cheese is bubbly and golden.
Once done, remove from the oven and let it cool for a few minutes before serving.
Serve the chicken broccoli bake hot as a main dish. It goes well with rice, pasta, or a side salad. Enjoy your meal!