Place a rack in center of oven and preheat oven to 375 degrees F. Lightly grease a deep 9-inch-square baking dish or a 3-quart casserole dish.
Bring the chicken stock to a boil in a large pot, then add the rice. Return to a boil, add the broccoli to the top of the rice (no need to stir it together), then cover, reduce the heat to low, and let cook 5 minutes. Remove the pot from heat and let sit, covered, for an additional 5 minutes. Most of the rice liquid should be absorbed.
Meanwhile, heat the olive oil in a Dutch oven or other large deep pot over medium-high. Add the chicken, 1/2 teaspoon salt, 1/2 teaspoon garlic powder, and 1/4 teaspoon black pepper. Sauté until cooked through and no longer pink in the center, about 4 to 6 minutes, then remove to a plate. Being careful not to burn yourself, wipe the pot clean with a paper towel.
Reduce the heat to medium. In a small bowl or large measuring cup, whisk together the flour and 1/2 cup milk. Pour the mixture into the pot, then add the remaining 1 1/2 cups milk. Cook, stirring constantly until thickened, 7 to 10 minutes. Remove from the heat and whisk in the Dijon, remaining 1/4 teaspoon salt, 1/4 teaspoon garlic powder, and 1/4 teaspoon black pepper. Stir in the Greek yogurt and 1 cup of the shredded cheese until smooth.
Add the rice and broccoli mixture and the reserved chicken to the cheese sauce, stirring gently to coat.
Spoon the mixture into the prepared dish and top with the remaining 1/2 cup cheese. Bake 25 minutes until hot and bubbly. Let stand 10 minutes, then serve.