Attach food grinder attachment to electric stand mixer according to manufacturer's instructions. Grind peas and next 7 ingredients according to manufacturer's instructions using the coarse grinding plate.
Stir together crackers and flour in a small bowl. Stir 1/2 cup cracker mixture and egg into ground pea mixture until well blended. Reserve remaining cracker mixture.
Shape pea mixture into 18 (2-inch) cakes (about 1 1/2 tablespoons each), and place on a wax paper-lined jelly-roll pan. Cover and chill 30 minutes to 24 hours.
Pulse together hummus and sun-dried tomatoes in a food processor 5 to 6 times or until tomatoes are pureed.
Dredge cakes in reserved cracker mixture. Fry cakes, in batches, in hot oil in a large nonstick skillet 2 to 3 minutes on each side or until crisp and golden brown, adding more oil as needed. Drain on paper towels. Serve with hummus mixture and, if desired, pita bread, grape tomatoes, cucumbers, and arugula.
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