Preheat oven to 350 degrees F.
In a small bowl, beat the eggs and add the lemon pepper and salt. Dip the chicken breasts into the egg mixture and then in the Parmesan. Dip the artichoke hearts into the egg and then the Parmesan.
Line a large loaf pan with parchment paper, and place a layer of chicken breasts on the bottom of the pan. Cover the chicken with a layer of mortadella, salami, or prosciutto. Cover the ham with artichoke hearts, then with basil leaves, using all of the leaves. Repeat the layers of chicken, ham, and artichoke hearts. Cover with parchment paper or foil. Place a heavy weight on top of the terrine while baking to compress the layers. Place the loaf pan in a larger pan and pour in water to make a water bath. Bake for 1 hour 20 minutes.
Let the terrine cool completely at room temperature, then refrigerate in pan for several hours or overnight.
In a bowl, combine the mayonnaise, garlic, dill weed, and parsley and blend with a spoon. Chill the mayonnaise mixture.
To serve, carefully turn the terrine out of the pan onto a platter and slice 3/4-inch slices. Serve with chilled mayonnaise mixture and buttery crackers.