Preheat the grill to medium-high heat. In a small bowl, mix olive oil, garlic powder, onion powder, salt, and pepper. Brush this mixture over the chicken breasts.
Place the chicken on the grill and cook for about 6-7 minutes per side, or until the internal temperature reaches 165°F. Remove from the grill and let it rest for 5 minutes before slicing.
While the chicken is grilling, bring a pot of water to a boil. Add the broccoli florets and blanch for 2-3 minutes until bright green and tender-crisp. Drain and set aside.
In a separate bowl, combine Greek yogurt, mayonnaise, minced garlic, lemon juice, and dried dill. Mix until smooth to create the creamy garlic sauce.
To assemble the bowls, divide the cooked brown rice among four bowls. Top each with sliced grilled chicken, blanched broccoli, and a generous drizzle of creamy garlic sauce.