Try it stewed. In Puerto Rico we make it shredded "en salsa criolla" (literally means creole sauce) and use it to make lasagna-type dishes, or with pasta, with mofongo (fried mashed plantains) and so on.
Here's one of my recipes:
We also make it with bone'in pieces stewed with the same sofrito (onions, peppers, garlic and culantro) and potatoes, carrots, olives, (sometimes we add beer or white wine) and season with bay leaves and a little dried oregano. I will post a hub later.