Make the remoulade: Whisk all of the ingredients together in a small bowl. Cover and refrigerate for at least 30 minutes and up to 48 hours before serving to allow the flavors to meld.
Meanwhile, make the shrimp and fried green tomatoes: Heat 1 cup of the oil in a medium high-sided saute pan over medium heat until it reaches 350 degrees F on a deep-fry thermometer--or simply add a few grains of the cornmeal into the oil and if it sizzles, rises to top and turns golden brown quickly, the oil is ready.
Meanwhile, put the cornmeal and the buttermilk into 2 separate shallow baking dishes and season each with salt and pepper. Place a wire rack over a rimmed baking sheet.
Dip each tomato slice in the buttermilk and let the excess drip off, then dredge in the cornmeal, gently pressing to help it adhere to both sides. Place on the wire rack and let sit for 5 minutes.
While the tomatoes are resting, heat the remaining 3 tablespoons oil in a large nonstick skillet over high heat until it begins to shimmer. Season the shrimp with salt and pepper (and some spice mix, if using). Add half of the shrimp in a single layer and cook until golden brown on both sides and just cooked through, about 4 minutes. Remove with a slotted spoon to a plate. Repeat with the remaining shrimp.
Add the tomatoes to the high-sided saute pan in a single layer and fry until golden brown on both sides, about 2 minutes per side. Remove to the wire rack and immediately season with salt.
Top each tomato with 3 shrimp and some of the remoulade. Garnish with green onions or parsley.