Melt 1 tablespoon of the butter in a Dutch oven over medium-high heat. Add the diced onion and minced garlic and cook, stirring occasionally, until they become soft and translucent, about 5 minutes.
Add the soaked and drained lima beans, diced smoked ham, smoked ham hock, chicken broth, garlic powder, onion powder, bay leaves, thyme, rosemary, black pepper, and kosher salt to the pot. Bring the mixture up to a gentle boil.
Lower the heat to maintain a simmer and cook uncovered for 2 to 2 1/2 hours, stirring occasionally and adding more broth or water if the liquid becomes too low, until the beans are tender and the cooking liquid has thickened.
Remove and discard the bay leaves. Transfer the ham hock to a plate, pull the meat off the bone, shred it, and return the meat to the beans.
Stir in the remaining 3 tablespoons of butter until melted and incorporated. Taste and adjust seasoning with additional salt and pepper as needed before serving.