Place a pot over medium heat and place the mollejas (gizzards) inside with enough water to cover them. Cook until tender for up to 2 hours. Check every once in a while to see when they're done and add more water while cooking if necessary.
When they're done, drain the gizzards and leave them aside to cool.
If you decide to use green bananas, cook them as well by boiling them unpeeled in a pot of salted water until fork-tender. Remove the peel once cool enough and cut into 1/2-inch slices.
Once the gizzards have cooled enough that you won't burn yourself, start trimming away the excess fat or tough skin from around the edges and chop into smaller pieces.
Mix the chopped vegetables (including the green bananas, if using) with the vinegar, oil, bay leaves and seasoning in the pot with the mollejas and cook for around 5 minutes until the onion has softened.
Set aside and allow to cool to room temperature before serving. If making the dish in advance it can be kept in the fridge and served cold (it might taste even better after resting for a while!).