In a deep pot, cook the potatoes in the olive oil, turning occasionally, until brown, 5 minutes. Add the carrots and cook 2 to 3 minutes, stirring with a wooden spoon.
Add the tomato paste, stir, then add hot chicken stock, bay leaves and salt and pepper. Cover the pot and simmer for 40 minutes. Add the rice and cook 12 minutes longer or until rice is tender.
Remove and discard the bay leaves, adjust the seasoning and serve with sprinkled Parmesan cheese.