Cook the rice by boiling broth or water, adding rice and salt, then simmering 15 minutes. Stir in butter and let rest if slightly wet.
Roast broccoli at 400°F after tossing with oil, salt, and pepper. Cook 15–18 minutes until edges brown.
Season chicken with salt, pepper, and herbs, then sear in oil and butter for 5–6 minutes per side until golden and cooked through. Let rest.
Make the sauce by melting butter, sautéing garlic, adding cream, broth, and Parmesan, then simmering until thickened.
Return chicken to the sauce, warm through, and serve over buttered rice with roasted broccoli and extra sauce.