Trim off the stems and thorny tips of the artichoke. Put them in a deep pot and cover with water. Add salt, bay leaf, lemon halves, and crab boil. Bring to a boil over high heat. Reduce to medium heat and simmer until tender. Remove and drain. Cool slightly and remove the fuzzy choke from the center. Remove the leaves to expose the heart. Slice thinly and set aside.
Heat the oil in a skillet over medium-high heat. Add the onions. Season with salt and cayenne and cook, stirring, until the onions until soft, 2 to 3 minutes. Add the sliced artichokes and the garlic. Season with salt and cayenne. Cook for 1 minute. Add the crabmeat and cook for another minute. Remove and set aside to cool.
Make a batter by combining the eggs, milk, and baking powder in a mixing bowl. Mix well. Add the flour, 1/4 cup at a time, beating and incorporating until all of the flour is used and the batter is smooth. Season with salt, cayenne, Worcestershire sauce and hot sauce. Mix well. Stir in the parsley. Add the artichoke and crab mixture to the batter and fold to mix.
Heat the shortening to 360 degrees F. Drop the batter, a heaping tablespoon at a time, into the hot oil. When the beignets pop to the surface, roll them around with a slotted spoon in the oil to brown them evenly. Remove and drain on paper towels. Sprinkle the beignets with Essence. Serve with the Remoulade.
Yield: about 2 dozen