Add the rice and broth to a rice cooker and cook until done. Let sit on “warm” while you prep the rest of the dinner. (Alternatively, cook the rice in a saucepan according to package directions until tender, if done early, keep warm by storing in the oven or microwave).
As the rice cooks, add the carrots, celery, and onion to a large nonstick skillet along with 3 tablespoons extra virgin olive oil. Season generously with kosher salt and ground black pepper (about 1/2 teaspoon each). Cook over medium heat for about 30 minutes, stirring often, until the vegetables are nicely caramelized and golden brown.
Add the frozen peas and garlic to the pan, and cook, stirring often, for about 3 minutes, until the garlic is fragrant and the peas are defrosted. Transfer the entire mixture to a large serving bowl. Add the cooked rice, chopped parsley, fresh lemon juice, and parmesan cheese. Season with a sprinkle of salt and pepper and toss to combine. Set aside. (I put mine in the microwave to keep it warm, but putting it in a turned-off oven works too).
Next, sprinkle the cubed chicken with the flour and season with about 1/2 teaspoon each of kosher salt and ground black pepper. Sprinkle with the dried oregano and toss to coat the chicken evenly.
Add the 2 tablespoons fat or oil of your choice to the same skillet that you browned the vegetables in. Warm over medium-high heat and add the chicken (don’t add any of the extra flour from the plate, as it will burn). Cook, stirring occasionally, until well golden brown on all sides, about 10-15 minutes.
Add the golden chicken pieces to the rice mixture and toss to combine. Spoon into bowls, and serve.