Peel the shrimp and put the shells and heads into a saucepan with two quarts of cold water. Add the fennel, oregano, peppercorns and bay leaf. Bring the saucepan to a simmer for 30 minutes. Strain the stock, dispose of the solids. Reduce the stock over medium-low heat to about two cups. (Allow about an hour for this, during which you can make the grits, if you like.)
Make a blond roux with the butter and flour. Whisk in the reduced shrimp stock until the sauce thickens considerably. Add the brandy, tasso, and Tabasco chipotle pepper sauce. Add salt to taste. Stir well, cover, and keep warm.
Make the grits by bringing the half-and-half and the salt to a light boil. Stir in the grits and lower the heat to the lowest temperature. Cook, stirring now and then, until a furrow you make with a spoon drawn across the top surface remains for a few seconds. Stir the cheese into the grits until the cheese disappears. Keep the grits warm and covered.
In a large skillet, bring the sauce to a simmer and add the peeled shrimp. Cook for four to six minutes (depending on the size of the shrimp, stirring now and then, until the shrimp are firm and pink.
Stir the grits and spoon onto the plate. Surround or top the grits (your choice) with the shrimp and its sauce.
