Set a large, 6-quart stockpot or Dutch oven over medium-high heat, and add the peanut oil. Heat the oil to 350 degrees F. Fry the plantains in two batches until golden brown and crispy, about 2 minutes. Transfer to a paper towel lined platter and season lightly with salt.
Place a 1-gallon stockpot over high heat and fill with 2 quarts of water. Season the water with 1/4 cup of salt and bring to a boil. Once the water comes to a boil, add the shrimp to the pot and immediately turn off the heat. Let the shrimp sit until just cooked through, about 3 minutes. Remove the shrimp from the water and place on a sheet pan to cool.
Once the shrimp are completely cooled, chop into 1/2-inch pieces and place in a medium-sized stainless steel bowl. Add the lemon, lime and orange juices and stir in the cucumber, red onion and chiles. Refrigerate for 1 hour.
Stir the tomato, avocado, chopped cilantro, and olive oil into the shrimp mixture. Allow it to sit at room temperature for 30 minutes before serving.
To serve, divide the ceviche between 6 chilled martini glasses, garnish with 3 fried plantain strips and cilantro leaves.
Yield: 6 appetizer portions