For the remoulade: In a small mixing bowl, combine the mayo, shallots, scallions, mustard, cayenne, hot sauce, lemon juice, Worcestershire, a pinch of salt, and lemon zest. Adjust the seasoning with more salt and hot sauce if needed and reserve. Makes 1½ cups.
Fry the tomatoes: Bring cast-iron skillet to medium-high heat. Season the green tomato slices with salt. Set aside on a rack fitted over a rimmed baking sheet, which will later become the cooling rack after frying. Find 3 similarly shaped shallow baking dishes. In the first, add flour. In the second, pour the eggs. In the third, add cornmeal. We are creating an assembling line of dredging. One by one, flour a tomato slice on both sides, dunk in the egg mixture, and then dredge in the cornmeal. As you finish each tomato, stack them on a cutting board.When the skillet has preheated, add the oil and heat to shimmering. Fry the green tomatoes until golden, about 2 to 3 minutes per side.
Assemble the dish: When the tomatoes are crispy, golden brown, and heated through, place them on the cooling rack. Dollop a tablespoon of remoulade on a serving plate and arrange the fried green tomatoes over the sauce. Garnish with some arugula, more remoulade and serve immediately. Nobody wants soggy tomatoes!