Make broth: Heat olive oil in a heavy based large pot over medium heat.
Add crab shells and sauté until fragrant, about 8 to 10 minutes.
Add 10 cups water and all other ingredients. Bring to boil. Reduce heat to low. Simmer until broth is reduced to 9 cups.
This will take about 25-30 minutes. Strain broth through sieve lined with cheesecloth. Cool. Remove fat from top of broth.
Cook corn in a large pot of boiling salted water until tender, about 5 to 8 minutes. Drain and transfer to ice cold water.
When cold, cut off kernels and then purée in a blender with 1 cup water salt, and pepper.
Force purée through a very fine sieve into a bowl (discard solids).
Melt 3 tablespoons butter in heavy large pot over medium heat.
Add flour and stirring frequently, cook until mixture is golden brown, about 2-3 minutes. Gradually whisk in broth and corn purée.
Bring soup to boil. Simmer until flavors blend and soup thickens slightly, about 10 minutes. Season to taste with salt and pepper.
Add reserved crabmeat and 1/2 cup chopped parsley to soup. Simmer just until crabmeat is heated through, about 2 minutes.
Pour soup into bowls. Garnish with parsley sprigs and serve. Serves 10.