Preheat your oven to 375°F (190°C). Lightly grease a standard 9×13-inch glass or ceramic baking dish with non-stick cooking spray and set it aside.
Bring a small pot of water to a rolling boil over high heat. Drop in the chopped fresh broccoli florets and blanch them for exactly 2 minutes until bright green and slightly softened. Drain the broccoli into a colander and immediately rinse with cold tap water to stop the cooking process. Leave it to drain thoroughly.
Melt the 3 tablespoons of unsalted butter in a large skillet or saucepan set over medium heat. Add the diced yellow onion and sauté for 4 to 5 minutes, stirring often, until soft and translucent. Add the minced garlic and cook for 1 additional minute until highly fragrant.
Sprinkle the 3 tablespoons of all-purpose flour evenly over the sautéed onions and garlic. Stir continuously with a wooden spoon for 1 to 2 minutes to cook out the raw flour flavor, forming a thick paste.
Slowly pour in the chicken broth a little at a time, whisking vigorously to dissolve the flour paste completely and prevent lumps. Once smooth, whisk in the heavy whipping cream.
Bring the liquid to a gentle simmer over medium heat. Cook for 3 to 4 minutes, stirring frequently, until the sauce thickens into a rich, glossy gravy baseline that easily coats the back of a spoon. Turn off the stovetop heat entirely.
Stir in the Dijon mustard, garlic powder, onion powder, salt, black pepper, and exactly 1 ½ cups of the shredded sharp cheddar cheese. Whisk firmly for 1 minute until the residual heat completely melts the cheese into a uniform, velvety sauce baseline.
Add the cooked rice, diced chicken, and blanched broccoli florets directly into the skillet with the cheese sauce matrix. Use a large rubber spatula to fold the ingredients together gently until every grain of rice and broccoli piece is completely coated.
Pour the mixture straight into your prepared 9×13-inch baking dish, smoothing the top flat with your spatula.
Scatter the remaining ½ cup of shredded cheddar cheese evenly across the entire surface of the casserole.
Place the dish uncovered on the middle oven rack and bake at 375°F for 20 to 25 minutes. The casserole is finished the exact moment the interior sauce is bubbling fiercely around the edges and the top cheese layer is completely melted and lightly golden.
Remove from the oven and let it stand flat on a cooling rack for 10 minutes before scooping. This resting window allows the rich cheese matrix to tighten slightly so it serves beautifully. Serve hot.