Place mung beans into a large container and cover with several inches of cool water; let soak, 8 hours to overnight. Drain and rinse the beans.
Heat a Dutch oven over medium heat and add the olive oil. Stir in onion, carrots, and celery; cook until slightly soft, about 5 minutes. Increase heat to high and add the beans, chicken broth, water, ham bone, garlic cloves, garlic powder, and onion powder. Bring to a boil. Reduce heat to low; simmer, stirring occasionally, until beans are soft, about 45 minutes.
Take ham bone out of the pot and remove any meat still on the bone; return meat to the pot.