Start by rinsing the dry rice under cold water until the water runs clear. In a large saucepan, combine 1 cup of rinsed rice, ½ tsp salt, and 1 tbsp butter. Add 2 cups of water and bring to a boil. Once boiling, reduce the heat to low, cover, and simmer for about 18-20 minutes, or until the rice is fully cooked and the water is absorbed.
While the rice is cooking, heat the ½ cup of vegetable or canola oil in a large skillet over medium heat. Add the finely grated onion and sauté for about 5-7 minutes, or until the onion is translucent and fragrant.
In a mixing bowl, combine the beaten eggs, 1 tsp salt, 1 ½ cups milk, and 1 tsp dry mustard. Whisk together until well combined. Then, fold in the chopped parsley and shredded cheddar cheese.
Once the rice is cooked, fluff it with a fork and add it to the mixing bowl with the egg and cheese mixture. Gently combine all the ingredients until the rice is fully coated.
Preheat your oven to 350°F (175°C). Transfer the rice mixture into an oven-safe baking dish, spreading it out evenly. Bake for 25-30 minutes, or until the top is golden and the cheese is bubbly.
Once baked, remove the parsley rice from the oven and let it cool for a few minutes. Serve it warm as a delicious side dish.