Put 3 cloves garlic into a mortar and add 1 teaspoon salt. Mash with the pestle until it forms a smooth paste; set aside.
Bring a large pot of water to a boil. Cut both ends off the plantains and run a knife just through the skin down the sides. Drop them into the boiling water for 10 to 15 seconds. Take them out and plunge them into ice water. Peel the plantains and cut them into 1/2-inch thick slices.
Heat about 1/4-inch vegetable oil in a large skillet and fry the plantains, in batches, on both flat sides until browned, about 2 minutes per side. Remove with a slotted spoon and drain on paper towels. Press the tostones in a tostones press or on a cutting board with the bottom of a small heavy pot until they are about 1/4-inch thick. Toss them in a bowl with the garlic paste. Re-fry the tostones in the hot oil until golden brown.
Serve as is with a sprinkling of salt or with a dab of one of the suggested toppings.