Place the sliced onions in a bowl. In a separate bowl, combine the vinegar, sugar, lime juice and olive oil - stir until the sugar dissolves. Pour this mixture over the onions and let sit while you prepare the plantains.
Trim off both ends of each plantain. Use a sharp knife to score long the ridges of the plantain, making sure not to cut into the plantain itself. Remove the peel from the flesh of the plantain. Cut each plantain into 1 to 2-inch long pieces, and then slice each of these pieces in half lengthwise.
Rinse the plantains and place them in a pot, covering them with water. Add a tablespoon of salt and stir. Boil over medium-high heat for 30 minutes until fork-tender. Proceed to the next step while the plantains are boiling.
Once the plantains have 5-10 minutes left to boil, transfer the sliced onions and mojo liquid to a small saucepan, adding the garlic. Cook for 5-10 minutes until the onions become tender but still slightly crispy. Turn off the heat and cover the saucepan to keep the onions warm.
Once the plantains are soft, drain them, reserving about a cup of the cooking water. Place the plantains back in the pan, add butter, and mash until smooth and creamy. Gradually add reserved water (with a few teaspoons of mojo if desired), mixing until you achieve your desired texture. For a thinner, softer mangu, add more water. Season with extra salt if needed.
Top the mangu with the onions and serve right away.