Cut off the ends of each plantain. Make a vertical cut from the top to bottom of each plantain, then peel off the skin. Cut each plantain into 1-inch chunks.
Pour 1 cup of vegetable oil into a large skillet and bring heat to medium high. Add the plantains, flat side down. Cook for 4 minutes, then flip over with tongs and cook for 3 minutes on the other side. When they are done, place them on a paper towel to dry.
Place the fried plantains on a large cutting board and smash each one with a glass. Put them back into the frying pan and cook for 1 minute on each side. Put them on paper towels again to dry.
To make the sauce, put the garlic, mayonnaise, olive oil, lime juice, lemon juice, and salt into a small blender or food processor. Blend until smooth.
Serve the tostones with the garlic dip and fresh chopped parsley, if desired.