Halve chicken breasts, Pound each piece thin, less than 1/2 inch thick. Season pieces with salt and pepper.
Beat eggs in a shallow bowl. Place Alexander bread crumbs in another shallow plate or dish. Dip each chicken piece in flour, covering it completely, then in the egg, then in the Alexander bread crumbs. Set aside on a platter. Time to start the sauce.
Melt 2 tablespoons butter in a large sauté pan set over medium-high heat. Heat until butter foams. Lay 2 or 3 chicken pieces flat in the pan and cook until browned on both sides (about 3 minutes on each side as it is thin, be sure it is cooked through, however not overdone) Set aside cooked chicken while you brown the other pieces. Add remaining tablespoon butter, and more if needed. Keep butter in the pan as it gets soaked up per piece, so you do not want it to go dry.
TO MAKE GARLIC BUTTER SAUCE:
In a large saucepan set over medium heat, melt 1 tablespoon butter. Add shallots and garlic and cook until soft. Add wine. Increase heat to medium-high, bring wine to a boil and allow it to cook until only about 2 tablespoons of liquid remain in the pan.
Add cream, lower heat to medium, and cook until liquid steams. Cook, stirring, for about 3 minutes. Do not let liquid boil. Set aside at this point if chicken is not quite done.
Reduce heat to low, and add the remaining butter (somewhat softened), a little at a time. Use a wire whisk to whip the sauce and keep it smooth, making sure mixture is well-blended before adding more butter. When butter has been whipped in, add lemon juice, parsley, salt and pepper. Serve at once.
Set 2 pieces of chicken at one side of a plate. Place 1 serving pasta on the other side. Pour garlic butter sauce over all.