Heat the olive oil to medium-high heat in a deep pot. Sear the beef cheeks on all sides until a caramelized crust forms. Remove beef cheeks to a plate.
In the same pot, lower the heat to medium and add add onions. Cook for five minutes or until onions turn translucent. Add the carrots and the garlic, and cook for an additional 5 minutes. Stir in the tomato paste and thyme. Cook for another 5 minutes.
Place the beef cheeks back into the pot, and pour in the wine and water. Bring to a boil, then lower the heat to medium so that the liquid stays at a low simmer. Cook for 5 hours, or until beef is fork tender. Remove the meat from the pot. Discard the vegetables and cook the liquid down until it’s reduced in half. Season with salt and pepper to taste.