Preheat grill to 350°F with one burner off for indirect heat.
Cut potatoes, carrots, and Brussels sprouts into bite-size pieces. Drizzle with oil and mix in 1 tablespoon garlic powder, 1 tablespoon onion powder, and 1 teaspoon salt. Set aside.
Rub chicken with softened butter, remaining garlic powder, remaining onion powder, and remaining salt.
Place some veggies in the bottom of a Bundt pan. Place chicken on top of tube of Bundt pan. Fill pan with all the remaining veggies.
Place pan over indirect heat and grill 1 hour 30 minutes or until chicken reaches internal temperature of 165°F. Makes 4 to 6 servings.