Cut the chicken into bite-size pieces and season with salt and pepper. Set aside.
Preheat the oven to 375°F. Heat the olive oil in a large oven-safe skillet or Dutch oven over medium heat. Add the diced onion and cook for 4 to 5 minutes until softened. Stir in the garlic and cook for 30 seconds.
Add the chicken and cook for 3 to 4 minutes, stirring occasionally, until the outside is lightly browned (it does not need to be fully cooked).
Add the butter and let it melt, then stir in the flour. Cook for 1 minute, stirring constantly.
Pour in the chicken broth and milk, stirring well to smooth out the sauce.
Add the rice, tomato paste, onion soup mix, smoked paprika, and onion powder. Stir well, scraping up any browned bits from the bottom of the pan. Bring to a gentle simmer.
Cover tightly with a lid and transfer to the oven. Bake for 25 to 30 minutes, until most of the liquid is absorbed.
Check the rice. If it’s still slightly firm, cover and return to the oven for another 5 minutes.
Remove from the oven and stir in the frozen peas and carrots and Parmesan cheese.
Sprinkle the shredded cheese over the top, cover loosely, and return to the oven for 5 minutes, just until the vegetables are heated through and the cheese is melted. Finish with chopped green onions before serving.
Notes
Use the right rice: This works best with long-grain white rice. Brown rice will need more liquid and a longer cook time.Watch the salt: Onion soup mix adds plenty of salt, so go light when seasoning the chicken. Even if you use a store-bought packet of onion soup mix, use only 3 tablespoons to keep the dish from becoming too salty.Use a tight-fitting lid: If your lid leaks steam, the rice won’t cook evenly. If you’re unsure, use foil under the lid for a better seal.Don’t skip the simmer step: Make sure the liquid is at a gentle simmer before it goes into the oven. That jump-starts the rice so it cooks evenly.Adjust the texture: If you want it a little looser and creamier, add an extra splash of milk at the end.Check your pan size: A wide, shallow pan cooks faster than a deep pot. If your pan is smaller and deeper, it may need a few extra minutes.Let it rest: Give it 5 minutes after baking before serving. The rice finishes absorbing liquid and the texture settles.