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Peel the plantains, then cut them into 2 inch long chunks and place them into a bowl of cold salted water. This will prevent them from turning brown.
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Add about 1" of oil to a pan, and heat it to medium heat. Drain the plantains well, then slide them into the preheated oil (be careful, they may spatter a bit).
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Fry the plantain chunks on all sides, until they're tender in the middle (about 5-7 minutes). You'll know if they're cook through if you can slide a toothpick into the center with no resistance. Drain the plantains on a paper towel.
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Use a tostonera, a small pan or a small plate to press each plantain chunk until it's a flat disc that's about 1/4" thick.
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Once all the tostones are formed, pop them back into the oil, and fry them for 3-4 minutes more, flipping once, until they're golden and crispy on both sides.
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Drain the tostones on paper towels, then sprinkle lightly with kosher salt while they're still hot.
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Mix up the mayoketchup by combining the mayo, ketchup and garlic.
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Serve the tostones warm with the mayoketchup dipping sauce.