For the mayo: In a food processor, puree the basil, mayonnaise, lemon juice and mustard. Season with salt and pepper and set aside.
For the sandwich: Place the pancetta slices in a large nonstick saute pan set over medium heat and saute on both sides until crispy, about 3 minutes per side. Set aside on a paper towel-lined plate until ready to assemble the sandwich.
For the tomatoes: In a large shallow dish, add 1/4 cup flour. In a separate baking dish, beat the egg, buttermilk, baking powder and baking soda. In a separate large shallow dish, add the remaining 3/4 cup flour, cornmeal, salt and cayenne pepper.
Dredge the tomatoes in the flour, followed by the egg mixture and finally coat with the cornmeal mixture, shaking off any excess in between dredges. Place the tomatoes on a wire cooling rack set inside a rimmed baking sheet. Repeat the process with all the tomatoes.
Pour a 1-inch layer of vegetable oil into a cast-iron skillet. Heat the oil over high heat until it reaches 350 degrees F. Carefully add 4 tomato slices to the oil and fry until the tomatoes are golden brown, about 2 minutes on each side. Transfer the fried tomatoes to a baking sheet or plate lined with paper towels, season with salt and cool. Repeat with the remaining slices.
To assemble the sandwich: Slather each slice of bread with a generous amount of the basil mayo. Top 4 of the bread slices with 4 pieces of crispy pancetta, 2 fried green tomatoes and top with arugula. Finish by topping the sandwich off with the other slice of bread.