Place the peanut oil in a 4 to 5-quart Dutch oven and place over medium-high heat. Heat oil until it reaches 375 degrees F.
Rinse the squid thoroughly and pat dry. Cut the tentacles in half lengthwise and the tubes into 1/2-inch rings. Set aside.
Place the flour and the cornmeal into a medium mixing bowl and stir to combine. 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. Remove the squid and transfer to a cooling rack turned upside down set over a newspaper-lined 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 375 degrees F. Serve immediately.