Soak the beans covered by 3 inches of water in the fridge overnight or follow the quick soak directions here.
In a large deep pot, add the drained soaked beans, vegetable stock, water, bay leaf, quartered onion, and smashed garlic cloves.
Bring the pot of beans to a boil and then reduce to a simmer and cook uncovered 45 minutes to 1 hour. Check at 45 minutes. You want the beans to be tender but not overly soft. Add more water as needed if it begins to get low.
Once the beans are tender but not fully cooked, add the cumin, cayenne, and ½ tsp salt. Simmer for another 20-30 minutes to let the beans finish cooking and more liquid evaporate. If after 30 minutes the beans still seem too liquidy then continue cooking for a few more minutes.
When the beans are fully cooked, remove the large chunks of quartered onion and bay leaf from the pot. Now, add the olive oil and lime juice to finish. Then taste for salt and season as needed.
Serve the black beans with rice, in burritos, or as a side. Store leftovers in the fridge for up to a week or in the freezer for up to 3 months.
*The dried black bean soaking time was not taken into account in terms of the total time it takes to make the recipe.