Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
In a medium saucepan, combine the rice, 3 cups (720ml) of the chicken stock, and 1/2 teaspoon of salt. Bring to a boil, then reduce heat to low, cover, and simmer for 10 minutes. The rice will be partially cooked. Remove from heat and set aside, covered.
While the rice cooks, toss the chicken pieces in a bowl with the remaining 1/2 teaspoon salt, garlic powder, and paprika. Heat the olive oil in a large skillet over medium-high heat. Add the chicken and cook for 4-5 minutes, stirring occasionally, until lightly browned. The chicken does not need to be fully cooked through. Transfer the chicken to the prepared baking dish along with the raw broccoli florets.
Reduce the heat to medium and add the butter to the same skillet. Once melted, whisk in the flour to form a thick paste and cook for 1 minute, stirring constantly.
Slowly whisk in the milk until smooth, then whisk in the remaining 1 cup (240ml) of chicken stock. Bring the sauce to a simmer, whisking often, until it thickens, about 2-3 minutes.
Remove the skillet from the heat. Stir in 1 3/4 cups (200g) of the shredded cheddar cheese until it melts completely into the sauce.
Add the partially cooked rice to the baking dish with the chicken and broccoli. Pour the cheese sauce over everything and stir gently until well combined.
Sprinkle the top evenly with the remaining 3/4 cup (80g) cheddar cheese and all of the Parmesan cheese.
Bake for 25 minutes, or until the sauce is bubbly and the top is golden brown. A thermometer inserted into the thickest part of a chicken piece should read 165°F (74°C). Let the casserole rest for 10 minutes before serving.