Set a non-stick skillet over medium-high heat. Arrange the bacon in one layer and fry in batches until dark brown and crispy. Repeat with the remaining bacon. Set aside to drain on a plate lined with paper towels.
Fill a Dutch oven or skillet with 2 inches of vegetable oil and set over high heat. While the oil is getting hot, fill three shallow bowls with the flour, egg, and cornmeal, one ingredient in each. One at a time, dredge the tomatoes in flour, douse in egg, and then cover in cornmeal, shaking off any excess. Repeat with each slice.
Test the oil with one tomato—the oil should bubble vigorously upon contact and the slice should begin browning in less than a minute. Cook each tomato until golden brown and crispy, about one to two minutes per side, and remove with a slotted spoon to a plate lined with paper towels. Season generously with salt and pepper.
While the tomatoes are frying and draining, combine all the ingredients for the mayonnaise in a small bowl.
On a rimmed baking sheet, brush each slice of bread on both sides with olive oil. Place in the oven for a few minutes, until the bread is golden brown but not hard. Rub each slice with the garlic clove, and slather both halves with a thin layer of basil mayo. Top the first half with a small handful of arugula, two slices of bacon, and two or three slices of tomato. Top with the other slice of bread and push down to seal the sandwich.
Serve immediately, preferably with a side of coleslaw.