1. Prepare the Calamari: If using frozen calamari, thaw completely and pat dry with paper towels. Slice the tubes into 1/2-inch rings and pat dry again.
2. Make the Batter: In a medium bowl, whisk together the flour, cornstarch, baking powder, salt, and pepper. Gradually whisk in the ice-cold club soda or beer until just combined. Do not overmix; a few lumps are okay.
3. Fry the Calamari: Heat about 2 inches of vegetable oil in a large, heavy-bottomed pot or deep fryer to 350°F (175°C). Working in batches, dredge the calamari rings in the batter, shaking off any excess. Carefully add the battered calamari to the hot oil, being careful not to overcrowd the pot. Fry for 2-3 minutes, or until golden brown and crispy.
4. Drain and Serve: Use a slotted spoon to transfer the fried calamari to a plate lined with paper towels to drain excess oil. Serve immediately with lemon wedges and homemade mayonnaise.

Make the Homemade Mayonnaise:

1. Whisk the Yolk: In a medium bowl, whisk together the egg yolk, lemon juice, Dijon mustard, salt, and white pepper.
2. Slowly Add Oil: Begin whisking in the oil, a few drops at a time, until the mixture emulsifies and thickens. Once it starts to thicken, you can slowly drizzle in the remaining oil while whisking constantly.
3. Adjust and Serve: Taste and adjust seasonings as needed. If the mayonnaise is too thick, add a teaspoon of water or lemon juice.