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.