Preheat your grill pan or outdoor grill to high and the oven to 400ºF. Bring a large pot of salted water to a boil over high heat.
While waiting for the water to boil, get the potatoes started: Place the sliced potatoes on a baking sheet, season with 2 tablespoons grill seasoning and drizzle with EVOO. Place into the oven, cook until golden brown and tender, about 35 minutes.
While the potatoes are cooking, season the chicken breasts with the remaining 2 tablespoons of grill seasoning and drizzle with EVOO. Place on the grill and cook about 3-4 minutes per side, or until cooked through.
Once the water has come up to a boil, drop the broccoli into the salted water and cook until tender.