Using a sharp knife, dice chicken into 1/3″ thick pieces and place them in a large mixing bowl. Tip: If chicken breast is partially frozen, it will be a little bit easier to slice.
Into the mixing bowl, add remaining batter ingredients: 2 eggs, 1/3 cup mayonnaise, 1/3 cup flour, 1 1/3 cups shredded mozzarella, 1 1/2 Tbsp dill, 1/2 tsp salt and 1/8 tsp black pepper, or season to taste. Stir the mixture until well combined, cover with plastic wrap and refrigerate 2 hours or overnight.
Heat a large non-stick pan over medium heat and add 2 Tbsp oil. When oil is hot, add the chicken mixture a heaping Tablespoon at a time. Slightly flatten out the tops with the back of your spoon and sauté uncovered 3-4 min on the first side, then flip and saute 3 min on the second side or until outsides are golden brown and chicken is fully cooked through* Repeat with remaining fritters adding more oil as needed.
To make the aioli (if using), combine all ingredients in a small bowl or measuring cup and stir together until smooth.
Recipe Notes
*To test for doneness, cut a fritter in half and the chicken should be completely white inside. If your chicken patty is browning too fast, adjust your heat down.