Preheat the oven to 375°. Grease a 13x9-in. casserole dish.
Place ranch dressing, dill, parsley, garlic, Dijon mustard, smoked paprika, salt, pepper and cayenne pepper in the casserole dish; stir to combine.
Add broccoli, chickpeas, brown rice, vegetable broth and 1/2 cup sharp cheddar cheese; stir to combine, ensuring the rice is submerged in the liquid.
Cover; bake 25-35 minutes or until the rice is nearly tender. Uncover; top with the remaining 1 cup sharp cheddar cheese and mozzarella cheese. Bake an additional 10 minutes or until the cheese is melted and bubbly and the rice is fully cooked. Let stand 5 minutes before serving.