Place the peanut oil in a 5-quart Dutch oven fitted with a deep-fry thermometer and place over medium-high heat. Heat oil until it reaches 375ºF. Set a wire rack over a paper towel-lined half-sheet pan and set aside.
Rinse the squid thoroughly and pat dry. Cut the tentacles in half lengthwise and the tubes into 1/2-inch rings. Set aside.
Combine the flour and the cornmeal in a medium mixing bowl. In small handfuls, dredge the squid in the flour and cornmeal mixture and shake off the excess. In batches, gently lower the squid into the hot oil. Cook for 1 minute; the squid will not be browned, but lightly golden in color. Using a spider strainer, remove the squid and transfer to the prepared wire rack-topped half-sheet pan. Season with salt and pepper, as desired. Repeat until all of the squid is cooked. Make sure to check the temperature of the oil before each batch to ensure it is 375ºF. Serve immediately.