Cover the baking dish tightly with foil and bake for 20 minutes. This helps the chicken start cooking through and the broccoli begin to soften.
Carefully remove the foil and return the dish to the oven. Bake uncovered for another 15–20 minutes, or until the chicken is cooked through (internal temperature reaches 165°F/74°C) and the broccoli is tender.
Sprinkle the remaining 1/2 cup shredded cheddar cheese over the top. Place the dish back in the oven, uncovered, for 5–8 minutes, or until the cheese is fully melted, bubbling, and just starting to brown around the edges.
Let the cheesy broccoli chicken rest for about 5 minutes before serving so the sauce thickens slightly. Serve the chicken breasts topped with plenty of the cheesy broccoli and pan sauce from the dish.
For picky eaters, you can chop the broccoli into smaller pieces so it blends in more with the sauce, or serve the broccoli on the side from the pan and let kids scoop as much or as little as they like. If your family prefers milder cheese, use a mild cheddar or a Colby-Jack blend instead of sharp cheddar. To stretch the meal for more people, cut the chicken into large chunks before baking so it cooks a bit faster and everyone gets more cheesy broccoli mixed in; just start checking for doneness a little earlier. If you like a bit of crunch, sprinkle a handful of crushed butter crackers or plain breadcrumbs over the cheese for the last 5–8 minutes of baking. You can also swap in cream of chicken soup if you’re out of cream of broccoli, but the flavor will be slightly less “broccoli-forward.” Leftovers reheat nicely in the oven or microwave; add a tiny splash of milk before reheating to keep the sauce creamy.
