In a large pot of medium heat, heat the olive oil. Cook the onions until soft and translucent, about 5 to 7 minutes. Add the garlic and cook until fragrant, about 30 seconds additional.
Add the cubed chicken, and season with oregano, salt and pepper to taste and cook until the chicken is cooked, about 5-7 minutes.
Add the rice and cook with the chicken to lightly toast, about 1-2 minutes. Add the vegetables you're using (carrots, corn and peas), season with salt and pepper, then pour the chicken broth on top.
Mix all the ingredients together, bring to a boil, then reduce the heat to low, cover with a tight-fitting lid and simmer for 15 minutes, until rice is fully cooked. Remove from heat and allow the steam to continue cooking the rice for 5-10 more minutes.
Fluff the rice, stir in the parmesan cheese, if using, sprinkle with fresh parsley and serve warm.