Half fill a large pot with warm water. Add the ham, onion, bell pepper, celery, garlic, thyme, salt, and black pepper. Cover and boil over medium heat 30 minutes. Turn the ham over in the pot and boil another 20 minutes to cook and season evenly. Move the ham from the pot to a roaster pan, pour the broth over the ham, and sprinkle lightly with salt and pepper.