Rinse the brown rice under cold water until the water runs clear.
In a medium saucepan, combine the rinsed brown rice and 2 cups of water. Bring to a boil over high heat.
Once boiling, reduce heat to low, cover, and simmer for 25 minutes or until the rice is tender and water is absorbed.
While the rice cooks, preheat a grill pan or skillet over medium-high heat and brush with 1 tablespoon olive oil.
In a small bowl, mix ground cumin, smoked paprika, garlic powder, salt, and black pepper.
Pat the chicken breasts dry and evenly coat them with the spice mixture.
Grill the chicken breasts for 6-7 minutes per side or until fully cooked and internal temperature reaches 165°F (74°C).
Remove the chicken from the grill and let it rest for 5 minutes before slicing into strips.
Steam the broccoli florets until tender but still crisp, about 4-5 minutes.
In a large bowl, combine the cooked brown rice, steamed broccoli, diced red bell pepper, shredded carrots, and chopped green onions.
In a small bowl, whisk together the Greek yogurt, minced garlic, and fresh lime juice to make a creamy dressing.
Add the sliced chicken and chopped cilantro to the rice and vegetable mixture.
Drizzle the yogurt dressing over the bowl and gently toss to combine all ingredients evenly.
Divide the chicken and rice mixture into four bowls and serve immediately.