Preheat the oven to 375°F (190°C).
In a medium saucepan, combine the uncooked brown rice and low-sodium chicken broth. Bring to a boil, then reduce heat to low, cover, and simmer for 35-40 minutes until rice is tender and liquid is absorbed. Remove from heat.
While the rice cooks, heat olive oil in a large skillet over medium heat.
Add the chopped onion and sauté for 3-4 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Add the chicken breast pieces to the skillet and cook for 6-8 minutes until no longer pink, stirring occasionally.
Add the fresh broccoli florets to the skillet and cook for 3-4 minutes until they are bright green and slightly tender. Remove from heat.
In a medium bowl, whisk together the plain nonfat Greek yogurt, low-fat milk, Dijon mustard, dried thyme, black pepper, salt, and paprika until smooth.
Add the cooked brown rice to the skillet with the chicken and broccoli. Pour the yogurt sauce over the mixture and stir to combine evenly.
Transfer the mixture to a 9×13-inch baking dish and spread evenly.
Sprinkle the reduced-fat shredded cheddar cheese evenly over the top.
Bake uncovered in the preheated oven for 15 minutes until the cheese is melted and bubbly.
Remove from the oven and let the casserole rest for 5 minutes before serving.