Preheat oven to 400 degrees F and spray a baking dish with cooking spray.
Put the chicken in the baking dish and season with salt and pepper. Pour the hoisin sauce over the chicken and turn the chicken to coat evenly. Bake until opaque and cooked through, about 18 to 20 minutes.
Meanwhile, pour an inch or more of water in a skillet or wok and bring to a boil over medium-high heat. Place the broccoli stems in a bamboo or collapsible steamer. Set the steamer over the boiling water, cover, and cook 2 to 3 minutes. Add the florets and continue to cook just until the vegetables are crisp tender and bright green, 2 to 3 minutes more. Season with the salt and pepper.
Divide the chicken and broccoli among 4 plates and serve.
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