Soak the beans in plenty of water for at least 8 hours. Overnight is great.
Drain and rinse the soaked beans and place them in a large pot with 2 quarts of cold water and the bay leaves. Cover, bring to a boil, then lower the heat to medium. Simmer for 30 minutes, until tender but not fully cooked — the interior of the beans will still be grainy. Skim off any foam that collects while the beans are cooking. Reserve 1 cup of the bean cooking liquid and drain the rest. Keep the bay leaves with the beans for now.
While the beans are cooking, preheat the oven to 375°F.
Lightly oil a 4-quart Dutch oven or casserole dish. In the Dutch oven or a separate large saucepan, heat the garlic and oil over medium heat until the garlic starts to sizzle. Add the onion and stir until translucent and softened, 3 to 4 minutes. Add the carrot, stir, and cook for another minute. Add the tomatoes, reserved bean cooking liquid, vinegar, tomato paste, maple syrup, oregano, thyme, salt, and nutmeg. Stir and bring to a boil, then lower the heat and cook for 10 to 12 minutes to reduce the sauce a little. Taste and season with pepper and more salt if needed. Stir in the beans, parsley, and mint.
Transfer to the prepared casserole dish if not already using the Dutch oven. Cover and bake, stirring occasionally, for 30 minutes, until the beans are tender and creamy inside. Uncover and bake for an additional 10 to 15 minutes to reduce the sauce a bit and give the beans a slightly dry finish. Remove from the oven, discard the bay leaves, and serve.