Heat the oil in a large skillet over medium-high heat. Brown the pot roast on all sides.
Meanwhile, prepare the vegetables. Peel the carrots and cut them into 2-inch lengths. Peel the onion and cut it into wedges and mince the garlic.
Place the carrots and onion wedges in the bottom of the slow cooker.
Place the roast on the vegetables.
In a bowl, combine the canned tomatoes, tomato paste, minced garlic, basil, oregano, thyme, brown sugar, salt, pepper, and bay leaf. Pour the mixture over roast.
Cover and cook on low for 8 to 10 hours, or until the roast is very tender. Remove bay leaf before serving.