Heat the measured amount of stock needed in a saucepan, at least 2 quart sized.
While the stock is heating, heat a separate large skillet on medium high heat. Add the olive oil (or chicken fat if you have it) to coat the bottom of the pan. When the oil is hot, add the uncooked rice and brown the rice, stirring occasionally, for a couple of minutes.
When the rice has browned, add the onions and celery and cook a few minutes longer, until the onions begin to soften.
If you are using canned or boxed broth, be careful of how much seasoning you add. We usually use homemade, unsalted chicken stock, so we add 2 teaspoons of salt or seasoned salt along with ground pepper and a dash of cayenne.
If you are starting with seasoned broth, you may only need to add a teaspoon of salt. Taste test the broth/stock. It can be a little on the salty side because the rice will absorb a lot of the salt.
Pour the heated stock into the pan with the rice (or pour the rice mixture into the stock, depending on which pan has a lid).
Bring to a simmer, reduce the heat, cover, and cook for as long as the instructions say on your package of rice. Usually between 15 to 25 minutes. Use a timer.
After the set amount of cooking time, remove the pan from the heat and let sit for 10 minutes, covered. At no point during the cooking of the rice should you uncover the pan.
Fluff with a fork to serve. Stir in chopped parsley. You can also mix in heated peas, toasted almonds, or raisins to the pilaf to make it more interesting.