Bring enough water to generously cover the shrimp to a boil in a stockpot and add the shrimp. Boil for 3 minutes or until the shrimp turn pink. Drain and peel.
Bring the broth, milk, salt, and pepper to a light boil in a saucepan; do not bring to a full boil. Stir in the grits, reduce the heat and cover. Simmer for 10 to 15 minutes or until the creaminess has disappeared and the grits start to pull from the side of the pan. Then stir in the cheese, ham, butter, and chopped parsley.
Preheat the oven to 350 degrees. Fill greased tartlet pans ¾ full with the grits mixture. Bake for 15 to 20 minutes or just until the tops begin to brown. Insert 1 shrimp tail up into the top of each tartlet and bake for 8 to 10 minutes longer or until the grits are light brown. Garnish with sprigs of parsley.