Chicken Broccoli Rice Casserole

For the Rice

• 3 tablespoons unsalted butter
• 1 cup chopped yellow onion
• 1/2 teaspoon Diamond Crystal kosher salt
• 1/4 teaspoon freshly-ground black pepper
• 2 cloves garlic , minced
• 1 teaspoon chopped fresh thyme
• 1 teaspoon ground mustard powder
• 1/2 teaspoon sweet paprika (I use Hungarian paprika)
• 1 cup extra long grain white rice
• 2 cups chicken broth or stock (low- to moderate- sodium)

For the Broccoli

• 3-1/2 to 4 cups broccoli florets , 10 ounces (see note)
• 3 tablespoons water

For the Topping

• 1 cup crushed butter crackers (such as Ritz or Townhouse, about 30 crackers)
• 2 tablespoons unsalted butter , melted
• 2 tablespoons finely grated Parmigiano Reggiano
• 1/4 teaspoon sweet paprika
• 1/2 cup shredded cheddar cheese , 2 ounces (see note)
• Kosher salt and freshly-ground black pepper

For Assembling the Casserole

• 1-1/4 cups condensed cream of chicken soup (use homemade for the best flavor or a 10.5-ounce can if using store-bought--see note)
• 2 cups diced or shredded cooked chicken breast (such as from a rotisserie chicken), 12 ounces
• 1/4 cup finely-grated Parmigiano Reggiano
• 1-1/2 cups shredded sharp cheddar cheddar cheese , 6 ounces (divided)
• 1 cup half and half
• salt and pepper , to taste