Brine the beans: Place the beans in a large bowl with the 3 tablespoons of salt and water to cover by several inches. Let sit overnight or for 10 to 12 hours. Drain and rinse.
Place beans in a large pot with the remaining salt, the onion, thyme, garlic, and bay leaf. Cover with water by several inches. Bring to a boil, then reduce heat so water is gently simmering. Simmer until beans are cooked through, 45 minutes to 1 hour (or longer), adding water as necessary to ensure the beans are covered. Let beans cool in their cooking liquid. Store beans in their cooking liquid in fridge for a week or so. Store in freezer for months.