1. Place ham, onion, and dried pepper, if using, in a medium saucepan; add the water. Bring to a boil over medium-high heat, and reduce to a gentle simmer; cover, and cook 2 hours.

2. Using a slotted spoon or spatula, transfer ham and onion to a plate, and set aside; discard dried pepper. Return liquid to a boil over medium-high heat; cook, stirring occasionally, until liquid is reduced to 2 cups, about 45 minutes.

3. Meanwhile, shred any meat from the ham hock with a fork, and return to saucepan. Add sugar, stirring until dissolved. Reduce heat to medium; add green beans, and simmer, stirring occasionally, until beans are cooked through and most of the liquid has evaporated, about 8 minutes. Remove from heat, and season with salt and black pepper. Transfer to a serving dish. Serve hot.