Preheat the oven to 400°F.
Bring 1 cup water to a boil in a small saucepan. Stir in the quinoa, cover, and reduce the heat to medium-low. Cook until all the liquid is absorbed and the quinoa is fluffy, 12 to 15 minutes. Remove from the heat and allow to steam, covered, for at least 5 minutes.
Place the block of feta in the center of a 9 x 13-inch baking dish. Place the broccoli florets and cherry tomatoes around the feta. Nestle the chicken breasts into the vegetables, spreading everything into one even layer with the feta at the center. Drizzle with the olive oil and sprinkle with the garlic powder, salt, and pepper.
Bake until the chicken reaches an internal temperature of 165°F, about 30 minutes. The tomatoes should be jammy and the broccoli should be golden brown. Remove the cooked chicken from the dish and cut on a bias into ¼-inch-thick slices. Set aside.
With a wooden spoon, mash the block of feta and mix to combine with the broccoli and tomatoes. Add the cooked quinoa and fresh basil to the baking dish and mix well. Place the sliced chicken on top.
Spoon onto four plates. Garnish with more basil.
