Place pork neck bones in a large bowl; season with black pepper, adobo seasoning, and thyme. Cover with plastic wrap and let marinate in the refrigerator, about 1 hour.

Fill a large stockpot halfway with water. Add cooking wine, vinegar, cilantro, basil, onions, green bell peppers, and garlic. Cover and bring to a boil. Add pork neck bones. Reduce heat to low and cook, stirring occasionally, for 1 hour.

Stir potatoes into the pot. Cover and simmer, stirring occasionally, until neck bones and potatoes are tender, about 30 minutes more.