Preheat the grill to medium-high heat. While the grill is heating, prepare the chicken by patting it dry and seasoning both sides with garlic powder, onion powder, salt, and pepper.
Drizzle olive oil over the broccoli florets and season with salt and pepper. Set aside.
Once the grill is hot, place the chicken breasts on the grill and cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F. Remove from the grill and let rest for 5 minutes before slicing.
While the chicken is resting, grill the broccoli for about 4-5 minutes, turning occasionally, until tender and slightly charred.
In a small bowl, combine the Greek yogurt, mayonnaise, minced garlic, lemon juice, and dill (if using). Mix until smooth and creamy.
To assemble the bowls, divide the cooked brown rice or quinoa among four bowls. Top each bowl with sliced grilled chicken, grilled broccoli, and a generous drizzle of the creamy garlic sauce.