Place a soup pot over medium heat, then add the butter and oil.
When butter is melted, add in the shallots and sauté for 3 minutes (until translucent).
Add the chicken stock, heavy cream, and cayenne pepper powder. Mix thoroughly while bringing the pot to a simmer.
Lower the heat, then add in the crabmeat and tarragon and continue to cook the soup for 5 minutes.
Add the sherry, stir, and continue to cook the soup for 3 minutes.
Add salt and pepper to taste, then serve garnished with sprinkled cayenne powder and croutons.