Cook the rice: rinse 1.5 cups of rice under cold water, drain. Add to a medium pot, salt to taste, and add 3 cups of boiling water. Bring the water to the boil then cook over very low heat, covered, for 10 minutes (I would normally cook it for 15 minutes). The rice should be a little bit undercooked. You don't have to drain the rice.
Cook the broccoli: cut 1 lb (450g) broccoli into small florets, add to a large pot filled with salted water, cook for about 2-3 minutes, until partially soft and partially crunchy. Drain the broccoli and rinse with cold water.
Prepare the chicken: cut 4 medium chicken breasts into 1-inch (2-3 cm) cubes, season with salt, pepper, 1 Tbsp olive oil, 1 Tbsp Italian seasoning, and 1 Tbsp garlic powder. Set aside.
Make the mushroom sauce: Cut 1/2 lb (225g) mushrooms into 1/4-inch (5mm) half-slices. Heat 2 Tbsp butter in a big frying pan. Add the mushrooms in an even layer. Cook them over high heat for about 2 minutes, letting the mushrooms brown. Stir the mushrooms, then add all the other ingredients for the sauce (1/2 cup milk, 1/2 cup cream, 1/2 cup broth, 1 ts lemon juice, 1 ts Dijon mustard, 2 Tbsp flour), bring the sauce to the boil and cook, stirring for about 1 minute. Season to taste with salt and pepper.
Make the breadcrumb topping: Melt 3 Tbsp butter in a small pot, take the pot off the heat. Stir in 1/2 cup of breadcrumbs until combined, then 1/2 cup of grated Parmesan.
Preheat the oven to 375°F / 190°C / Gas Mark 5 (no fan, if you have a convection oven reduce the temperature by about 20° or follow the manufacturer's instructions).
Assemble the casserole: Add the cooked rice, broccoli, uncooked chicken, 1/2 cup of grated cheddar cheese, and mushroom sauce into a 9x13 inch (23x33 cm) casserole dish and mix together. Top with the remaining grated cheddar, then with the breadcrumb topping.The sauce should be hot, straight from the pan, otherwise, it may take longer for the casserole to heat through and you will need to bake it longer.
Bake (uncovered) for about 25-30 minutes or until the breadcrumb topping is golden and the chicken is cooked through. Try to not cook it longer to not overcook the chicken. If after this time the topping is not golden yet, you can turn on the fan or move the baking dish under the broiler to quickly brown the topping.
Set aside for 5-10 minutes before cutting into servings to allow the casserole to set a little.