Place the chicken on a large baking sheet. Pat it dry and score the top of each chicken breast in a crosshatch pattern, being careful not to cut all the way through.
Drizzle with 2 tablespoons olive oil and season with the garlic powder, onion powder, paprika, salt, and pepper. Rub the seasoning evenly over the chicken.
Arrange the broccoli around the chicken. Drizzle with the remaining 1 tablespoon olive oil and season with salt and pepper.
Bake for 18–23 minutes, or until the chicken reaches 165°F in the thickest part.
In a small bowl, whisk together the Dijon mustard, honey, apple cider vinegar, and olive oil.
Remove the baking sheet from the oven and brush the chicken and broccoli with the honey mustard glaze.
Broil on high for 2–3 minutes, watching closely, until the glaze is lightly caramelized. If you don't want to broil, you can bake for another 2–3 minutes instead.
Serve the chicken and broccoli with any remaining honey mustard glaze.