Prepare the chicken: Cut the breasts into third-inch-thick slices. Tip: It's easier to slice chicken that's partly cold.
Chicken, eggs, mayonnaise, flour, mozzarella, dill, salt, and pepper should all be mixed together in a big bowl. Mix well. Put the mixture in the fridge for at least two hours.
Melt butter in a nonstick pan over medium-low heat. Add oil and heat it up. Put a few tablespoons of the chicken mix into the pan and spread it out a bit. For three to four minutes on each side, or until golden brown and cooked all the way through.
Aioli Dip: Blend all the aioli ingredients together until the sauce is smooth.
Note: Before you serve the chicken, make sure the inside is completely white. Change the heat if the fritters get brown too fast.