Open the chicken package and place chicken, breast side up, in the middle of a baking sheet. Discard package and marinade.
Rinse and dry potatoes. Cut potatoes into bite-sized pieces and place in a min bowl. Drizzle with 2 tablespoons olive oil, 1/2 teaspoon salt, 1/4 teaspoon pepper, and paprika. Stir to coat. Spread potatoes around the chicken. Place in the hot oven and set a timer for 30 minutes.
While the chicken gets started, chop broccoli into florets and place in the same bowl you used for the potatoes. Set aside.
Start the sauce by placing a medium saucepan over medium heat. Add 2 tablespoons olive oil. Once hot, add onions, garlic, and ginger. Cook for about 5 minutes until translucent and soft, stirring often.
Add brown sugar and stir until sugar melts and becomes sticky. Pour in orange juice, tomato sauce, and ginger beer. Stir to combine. Bring to a simmer and cook for 15 minutes, stirring occasionally, until your desired consistency is reached. (The sauce will be thin.)
Your timer will go off while the sauce is cooking. When it does, take the baking sheet out of the oven. Use a wooden spoon to stir the potatoes around. Toss the broccoli in 1 tablespoon olive oil and remaining salt and pepper. Spread broccoli around the pan and return it to the oven. Set timer for another 30 minutes.
Add apple cider vinegar, Worcestershire sauce, and pepper and stir to combine. Use the sauce as is or use an immersion blender to puree the onions into the sauce. (A regular blender can be used as well.)
The sauce should be done with about 20 to 25 minutes left in the roasting time. Brush sauce all over the chicken 3 to 4 times while it finishes roasting.
Once cooking time is up, use a meat thermometer to check the internal temperature of the chicken is 165 degrees F. Stick it in the thickest part of one of the breasts. If meat is done, remove from oven and rest 5 minutes.
Transfer chicken to a cutting board and break down into two leg/thigh and two breast/wing portions. Plate one portion on each dinner plate. Divide potatoes and broccoli amongst the plates. Serve warm with extra sauce on the side for dipping.
Notes
Nutrition information is an approximation based on the raw nutrition of the chicken for 4 ounces. Each serving assumes 10 ounces of cooked chicken.
Nutrition information also assumes ALL of the sauce will be eaten. You'll only need to use about 1/4 to 1/3 cup of the sauce to baste the chicken. Leftover sauce can be stored in an air-tight container in the fridge.