In a deep pot or large saucepan, heat the olive oil over medium heat.
Add the potatoes and cook, turning occasionally, until browned, about 5 to 10 minutes.
Add the onions, carrots, and celery. Cook for 2-3 minutes over medium heat, stirring with a basting spoon or wooden spoon. (Note: Potatoes may stick slightly to the bottom of the pan, but don't worry; they’ll take on added flavor as long as you don’t let them burn.)
Add the minced garlic and cook for 1 minute.
Add the chicken bouillon and tomato paste and stir well.
Pour in the hot water, add the bay leaves, and season with pepper.
Cover the pot and simmer over medium-low heat for 40 minutes, stirring occasionally.
Add the rice and continue to cook for 12 minutes, or until the rice is tender.
Remove and discard the celery and bay leaves.
Taste and adjust the seasoning as needed before serving.