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Preheat oven to 350 degrees. In a large pot of boiling salted water, cook pasta according to package instructions; drain.
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Meanwhile, in a large bowl, combine 1/2 cup breadcrumbs, milk, 1 teaspoon salt, and 1/4 teaspoon pepper. Add chicken and stir until just combined (do not overmix). In a medium straight-sided skillet, heat oil over medium until it registers 350 degrees on a deep-fry thermometer.
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Place remaining 1 1/4 cups breadcrumbs in a shallow dish. Divide chicken mixture into 4 portions and flatten each into a disk. Place 4 mozzarella pieces in center of each, then form disk into a ball around cheese. Coat balls in breadcrumbs and fry until golden brown, 5 minutes, turning once. With a slotted spoon, transfer meatballs to a paper-towel-lined rimmed baking sheet and let drain 1 minute.
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Discard paper towels and transfer sheet to oven. Bake meatballs until chicken is cooked through, about 14 minutes. Divide pasta among four bowls and top each with marinara and a meatball. Sprinkle with parsley.
