Combine shrimp,breadcrumbs,egg,egg yolk,parsley,cracker meal,garlic and cayenne pepper in a processor. Using on/off turns, process until shrimp is finely chopped but not pasty. Form mixture into 24 balls,using 2 tbsp for each. Roll balls into cracker meal.
Pour vegetable oil to depth of 3 inches in heavy large pot. Heat oil to 325. Working in batches,fry shrimp balls until golden brown,turning occasionally,about 5 minutes. Using slotted spoon,transfer shrimp balls to paper towels and drain.
Place 3 shrimp balls on bottom half of each roll. Top with tartar sauce,lettuce and tomato,then roll tops. Serve immediately,passing hot sauce separately.
*Ground saltine crackers would work in place of cracker meal