In a food processor, combine the mayonnaise, anchovies, lemon juice, parsley and cayenne. Blend until smooth. Transfer the sauce to a bowl and refrigerate, covered tightly, for up to 2 days, until ready to serve.
Cut the squid into 1/3-inch rings. If the tentacles are large, halve or quarter them lengthwise. Refrigerate until ready to use.
In a heavy bottomed straight sided 3 quart saucepan, about 8 inches in diameter, heat the oil to 360 degrees.
In a shallow bowl, combine the flour and graham cracker crumbs. Toss 1/3 of the squid in the flour mixture to coat evenly. Shake the squid in a mesh strainer to shed extra coating. Using tongs or a slotted spoon, gently lower each batch of calamari into the hot oil and fry until golden brown, about 2 minutes. Remove with a slotted spoon and drain on paper towels. Sprinkle with salt.
The cooked squid can be kept warm in a low oven while you continue. Check your oil temperature and repeat with remaining calamari. Serve hot with chilled anchovy mayonnaise.
Adapted from a recipe in the Union Square Cafe Cookbook,