Combine the first 10 ingredients in a food processor with a metal blade and process until smooth. Season with salt, cayenne, and pepper. While the machine is running, slowly add the oil, a little at a time, until thick. Reseason if needed.
*RAW EGG WARNING
Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness. To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.
Combine all ingredients thoroughly and store in an airtight jar or container.
Yield: about 2/3 cup
Recipe from New New Orleans Cooking, by Emeril Lagasse and Jessie Tirsch. Published by William and Morrow, 1993.
Season the rock shrimp with Essence. Prepare the smoker according to manufactures? directions. Add the shrimp and smoke for about 8 to 10 minutes. Remove from the smoker and cool.
Heat the oil in a skillet over medium-high heat. Add the onions and season with Essence. Saute for about 3 minutes, or until slightly wilted. Add the corn and season with Essence. Continue to saute for 3 minutes. Add the shrimp and saute for 2 minutes. Add the garlic. Remove and set aside to cool.
Make a batter by combining the eggs, milk, baking powder, and salt. Add the flour, 1/4-cup at a time, beating and incorporating until all is used and the batter is smooth. Season with hot sauce and Worcestershire sauce. Stir in the parsley. Add the shrimp 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 the Essence. To serve, spoon the Remoulade in the center of a large serving plate. Arrange the beignets on top of the sauce. Garnish with the cheese and green onions.