Prepare the vegetables by finely dicing the yellow onion, green bell pepper, and celery, and mincing the garlic so they are ready to go when you start cooking.
Rinse the long-grain white rice under cold water until the water runs mostly clear, then drain it well and set aside.
Heat the olive oil in a large deep skillet or wide saucepan over medium heat.
Add the ground beef to the skillet and cook, breaking it up with a spoon, for about 5 to 7 minutes until it is browned and no longer pink.
If there is excess fat in the skillet, carefully spoon off a bit, leaving about 1 to 2 tablespoons so the rice and vegetables have some flavor to cook in.
Add the diced onion, green bell pepper, and celery to the browned beef and cook for 4 to 5 minutes, stirring often, until the vegetables start to soften.
Stir in the minced garlic and cook for about 30 seconds, just until fragrant, so it does not burn.
Add the rinsed and drained white rice to the skillet and stir well, letting the rice toast lightly in the mixture for about 1 to 2 minutes.
Sprinkle in the kosher salt, black pepper, paprika, dried oregano, dried thyme, and cayenne pepper, and stir until the beef, vegetables, and rice are evenly coated with the seasonings.
Pour in the low-sodium beef broth and stir, scraping the bottom of the skillet gently to release any browned bits into the liquid.
Bring the mixture up to a gentle boil over medium-high heat, then reduce the heat to low so it simmers softly.
Cover the skillet with a tight-fitting lid and let the dirty rice cook undisturbed for 18 to 20 minutes, or until the rice is tender and most of the liquid is absorbed.
Once the rice is cooked, turn off the heat and let the skillet sit, covered, for another 5 minutes to allow the steam to finish cooking the rice and to help everything settle.
Remove the lid, fluff the dirty rice gently with a fork to separate the grains, and stir in the chopped fresh parsley.
Taste and adjust the seasoning with a little more salt or black pepper if needed, then serve the dirty rice with ground beef hot.