Place chicken breasts, one at a time, between 2 sheets of wax paper or plastic wrap. With flat side of a mallet, gently pound breasts until each is about 1/4 inch thick set aside.
In a rimmed plate or pie pan, combine bread crumbs, parmesan cheese, 1 teaspoon of the oregano, garlic salt, and pepper set aside. In a small bowl, stir together the 4 tablespoons softened butter, parsley, and the remaining 1/2 teaspoon oregano.
Spread about 1/2 tablespoon of the herb-butter mixture across each breast about an inch from lower edge lay a strip of jack cheese over butter mixture. Fold lower edge of brease over filling then fold in sides and roll up to enclose filling. Dip each bundle in the melted butter and drain briefly then roll in bread crumb mixture until evenly coated. Place bundles, seam side down, without touching, in a 9x13 inch baking pan. Drizzle with any remaining butter. Cover and refrigerate for at least 4 hours or until next day.
Bake, uncovered, in a preheated 425° oven for 20 minutes or until chicken is no longer pink when lightly slashed (cut just a small slash so filling doesn't ooze out.)