Preheat the oven to 375 degrees F. Grease or spray, using non-stick baking spray, a 9 x 13-inch baking casserole dish.
Using a medium sized saucepan over medium-high heat, bring the broth to a boil. Add the orzo and cook until almost tender, for about 7 minutes, turning the heat down to medium-low once the orzo has been added and mixing occasionally so the orzo does not stick to your saucepan. Most, if not all, of the broth will be absorbed into the orzo. Remove from heat and set aside.
Using a large skillet over medium-high heat, heat the olive oil and add the onions and saute until tender, for about 3 minutes. Add the mushrooms and broccoli and continue to saute for about 5 to 6 minutes.
Turn the heat to low and add in the cooked orzo and any remaining broth. Pour in the heavy cream and the parmesan, mozzarella, cheddar cheese and cooked chicken and mix well to combine everything. Remove from the heat and season with salt and pepper and stir to combine. Pour the mixture into the prepared baking casserole dish.
Sprinkle on a little more parmesan over the top if desired and bake until golden and the cheese has melted, for about 20 to 25 minutes. Allow to cool slightly before cutting and serving. Enjoy while hot.