How to Make It
Bring a large pot of water to a boil over high heat. Add corn; boil 3 minutes. Remove corn from pot; let stand 5 minutes. Cut kernels from cobs. (You should have about 4 cups kernels; set aside 1/2 cup.)
Combine 3 1/2 cups corn kernels, tomatoes (set aside a few to chop for garnish, if desired), and next 7 ingredients in a blender; process until smooth. Add cream; process until just combined. Pour mixture into a bowl; cover and chill at least 2 hours.
Divide gazpacho evenly among 4 soup bowls; top with crab. Sprinkle evenly with green onions, reserved 1/2 cup corn kernels, and reserved chopped tomatoes, if desired.