Combine beans, garlic, onion, bay leaves, and oregano in a medium pot. Add enough water to pot to cover beans by about 1 1/2 in.
Bring to a boil over medium-high heat. Reduce heat and simmer gently, covered, until beans are tender, 1 1/2 to 2 hours, adding more water if needed to cover beans by 1/2 in. They should be soupy when cooked.
Season beans to taste with salt and pepper and serve in their cooking liquid.
*Mexican oregano is more intense than regular Italian oregano; find it in well-stocked grocery stores, Latino markets, and online.
Make ahead: Up to 5 days, cooled in cooking liquid and then chilled in the liquid.