Heat the olive oil and butter in a large, deep skillet over medium heat. Add the chopped onion and cook for about 4 minutes, stirring occasionally, until softened and lightly golden.
Add the grated carrot and cook for about 6 minutes, stirring occasionally, until the vegetables are tender and fragrant.
Add the ground beef and break it apart with a wooden spoon. Cook for about 12 minutes, until browned and most of the excess moisture has evaporated.
Season with salt, black pepper, dried basil, and oregano. Stir in the chopped garlic and cook for another 4 minutes, stirring often so the garlic does not burn.
Add the rinsed and well-drained rice. Cook for about 4 minutes, stirring gently, until the grains are coated in the savory beef mixture.
Pour in the hot water or broth and add the bay leaves. Stir gently to distribute the rice evenly.
Bring the liquid to a gentle simmer, then reduce the heat to low and cover the skillet. Cook without lifting the lid for about 25 minutes, or until the rice is tender and the liquid has been absorbed.
Remove the skillet from the heat and let it rest, covered, for 5 minutes. Remove the bay leaves, gently fluff the rice with a fork, and serve warm.