Whisk together the chopped jalapenos, mayonnaise and 1 teaspoon of reserved pickling liquid. Season with salt and set aside.
Rinse the calamari under cold running water and lightly pat dry, leaving it slightly damp. Leave the tentacles whole and cut the bodies crosswise into 1/4-inch wide rings.
Heat the oil in a heavy pot over high heat until it registers 375 degrees F on a thermometer.
Place the panko in a shallow bowl and season with salt and pepper. Dredge a small handful of the squid rings in the panko, tossing to coat well. Shake off any excess and, with a slotted spoon, add the rings to the oil, using the spoon to separate the rings. Cook until golden, 1 to 2 minutes. Using the slotted spoon, transfer the rings to paper towels to drain. Season with salt and pepper. Repeat with the remaining ingredients. Serve with the pickled jalapeno dipping sauce.
BYOC: Don't love the heat? Try substituting your favorite pickled item for the jalapenos.