For the gazpacho: Place the tomatoes, cucumbers, chiles, shallots, garlic, vinegar, hot sauce, and salt in a blender. Blend until smooth. Taste and adjust the seasoning with salt, to taste. Refrigerate for 2 hours until ready to serve.
For the croutons: In a large heavy-bottomed saucepan, pour enough oil to fill the pan with 1 inch of oil. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 375 degrees F. (If you don't have a thermometer, a cube of bread will brown in about 3 minutes.) Working in batches, carefully add the polenta cubes and fry, stirring occasionally to keep the cubes separated, until golden brown, about 2 minutes.
Drain on paper towels and sprinkle with the Parmesan.
To serve: Ladle the gazpacho into 4 soup bowls and top with the polenta croutons.