Preheat the oven to 375°F (190°C).
Heat the olive oil in a large skillet over medium heat, then sauté the minced garlic for about 1 minute until fragrant.
Add the chicken broth, heavy cream, lemon juice, fresh thyme or rosemary, red pepper flakes, and salt and pepper to the skillet and bring the mixture to a simmer.
Stir in 1/2 cup of the grated Parmesan until combined, then remove the sauce from the heat.
In a large 9×13 casserole dish sprayed with cooking spray, combine the uncooked rice, broccoli florets, and the cut chicken pieces; season the chicken with additional salt and pepper if desired.
Pour the hot lemon-Parmesan sauce evenly over the rice, broccoli, and chicken, stirring lightly to coat everything.
Sprinkle the remaining 1/2 cup Parmesan and the breadcrumbs evenly over the top of the casserole.
Tightly cover the dish with foil and bake for 35 minutes, then remove the foil and bake an additional 10 minutes uncovered until the chicken is cooked through and the rice has absorbed the liquid.
Remove from the oven and let the casserole rest for 5 minutes before serving.