Preheat oven to 350°F.
Cut or break broccoli florets into bite-size pieces. Utilize the broccoli stem by trimming and discarding the tough outer layer by slicing about 1/8 inch from the perimeter. Then, cut the remaining light green stem into bite-sized pieces. Place broccoli onto a baking tray or in a large oven-safe dish.
Add the shredded cabbage to the broccoli dish and season with oil, salt, pepper and garlic powder and mix well. Roast in the oven until cooked, about 15-20 minutes.
Dry chicken with a paper towel (this encourages browning when sautéed.) Cube chicken in bite-size pieces and place in a bowl. Season chicken cubes with oil, salt, pepper, garlic powder and onion powder.
Rinse quinoa well until water runs clear. Then cook according to package instructions.
Heat a large sauté pan over medium-high heat. Add seasoned chicken in a single layer making sure not to overcrowd the pan. Cook until browned, about 3-4 minutes. Then flip chicken to brown the other side, another 3-4 minutes.
While the chicken, quinoa and vegetables are cooking, add vinaigrette ingredients to a jar and shake well to incorporate. Taste and adjust seasoning to taste.
Once all ingredients are cooked, quinoa to a bowl, add the vegetables and chicken and top with a little vinaigrette on top.