Sear the ham hock. Heat olive oil in a heavy caldero or Dutch oven over medium-high heat. Add the ham hock and brown on all sides, about 5 minutes total. Remove and set aside.
Bloom the sofrito. Reduce heat to medium. Add the sofrito and tomato paste to the same pot. Cook, stirring constantly, until the mixture darkens significantly and the raw smell of garlic is gone, 8 to 10 minutes. This is the step nobody can skip. Every minute matters.
Return the ham hock. Place the seared ham hock back in the pot. Pour in the bone broth. Add the bay leaf, oregano, and culantro stems.
Simmer. Bring to a gentle boil, then reduce to low. Partially cover and simmer for 25 minutes, until the ham hock is tender enough to pull apart easily.
Add beans and calabaza. Stir in the kidney beans and diced calabaza. Continue simmering 15 to 20 more minutes, until the calabaza has dissolved into the broth and the beans have absorbed the flavor.
Shred and return. Remove the ham hock to a cutting board. Pull off the meat, shred or chop it, and return it to the pot. Discard the bone and skin (or save the bone for your next batch of bone broth).
Finish. Taste and adjust salt and pepper. Remove the bay leaf and culantro stem. Serve immediately, garnished with fresh cilantro and a squeeze of lime.