In a large bowl, whisk the cornmeal with the flour, sugar, baking soda, salt, oregano, cayenne pepper and black pepper. In a medium bowl, whisk the eggs with the milk, scallions and the 1 tablespoon of vegetable oil. Stir the wet ingredients into the cornmeal mixture until just blended. Cover and refrigerate the batter for 1 hour.
In a medium bowl, whisk the mayonnaise with the mustard, ketchup, cider vinegar, shallot and scallion. Season the remoulade with Tabasco, salt and pepper.
In a medium saucepan, heat 2 inches of oil to 325°. Set a large rack over a baking sheet. Drop 6 rounded tablespoons of batter at a time into the hot oil and fry, turning once, until the hush puppies are browned and crisp, about 2 minutes. Using a slotted spoon, transfer the hush puppies to the rack to drain. Serve the hush puppies hot with the remoulade.