In a deep pot or large saucepan, cook the potatoes in the olive oil, turning occasionally, until browned, about 5 minutes. Add the carrots and celery, and cook 2-3 minutes over medium heat, stirring with a wooden spoon. (The potatoes may stick slightly to the bottom of the pan. No harm done—in fact they’ll take on added flavor—so long as you don’t let them burn.) Add the tomato paste, hot chicken stock, bay leaves, and salt and pepper. Cover the pot and simmer 40 minutes over medium-low heat. Add the rice and cook 12 minutes longer, until the rice is tender. Remove and discard the celery and bay leaves, adjust the seasoning, and serve sprinkled with grated cheese.