Preheat a grill pan over medium-high heat.
Place potatoes in a large enough pot to accommodate both the potatoes and the broccoli, and cover them with cold water. Bring to a boil, add some salt, then reduce the heat a bit and cook until tender, about 12 minutes. Halfway through, add the broccoli.
Drizzle the chicken pieces with EVOO and sprinkle with grill seasoning. Add the chicken pieces to the hot grill pan and cook 6 minutes on each side.