In a large skillet, heat the olive oil over medium heat. Add the chicken and onions, and season lightly with salt and pepper. Sauté, stirring frequently, just until the chicken is no longer pink on the outside and the onions have begin to soften. Note: The chicken will not be cooked all the way through at this point because it will continue cooking with the rice.
Add the garlic; sauté,, stirring frequently, for another minute.
Add the rice and sauté, stirring frequently, for about 2 minutes.
Combine the roasted chicken base and water; add to the skillet. Bring to a boil; reduce the heat, cover, and simmer for 10 minutes.
Scatter the broccoli on top of the chicken mixture (don't stir).
Cover and continue simmering for an additional 10 minutes or until the liquid is absorbed and the rice is tender. The broccoli should also be crisp-tender at this point.
While the mixture is simmering, preheat the broiler.
Add ½ cup of the cheese to the chicken mixture and stir to combine. Taste and adjust the seasoning if needed.
Top the chicken mixture with the rest of the cheese.
Combine the melted butter and panko breadcrumbs; scatter them evenly over the top of the cheese.
Broil until the cheese is melted and the breadcrumbs are golden brown.