Heat the oil and butter in a large skillet over medium heat. When the butter is melted, add the chopped onion. Cook, stirring occasionally until the onion is softened, about 6 to 7 minutes. Add the garlic and cook for one minute.
Add the rice and orzo to the skillet. Stir to combine with the onion mixture. Continue cooking and stirring until the rice is toasted/golden brown.
Pour in the heated chicken stock and add the cayenne pepper.
Stir, bring to a boil, then reduce heat to low. Cover the skillet and simmer for 20 to 25 minutes.
Remove from heat and fluff rice with a fork. Stir in the parsley, season with salt and pepper, and serve.