Heat olive oil in a large skillet over medium heat.
Add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the ground chicken to the skillet and cook, breaking it apart with a spatula, until browned and cooked through, about 5-7 minutes.
Stir in the diced zucchini and cook for 2 minutes until slightly softened.
Add the rinsed rice, dried oregano, smoked paprika, salt, black pepper, and crushed red pepper flakes to the skillet. Stir to combine.
Pour in the chicken broth and bring the mixture to a boil.
Reduce heat to low, cover the skillet with a lid, and simmer for 15 minutes until the rice is tender and liquid is absorbed.
Remove the skillet from heat and let it sit covered for 5 minutes.
Fluff the rice with a fork and stir in the grated Parmesan cheese and chopped fresh parsley.
Serve warm.