In a mixing bowl, combine all-purpose flour, whole-wheat or all-purpose flour, and baking soda. Set aside.
In a large mixing bowl, beat peanut butter and butter with an electric mixer on medium speed for about 30 seconds. Add granulated sugar and brown sugar; beat until fluffy. Add thawed egg product or egg and vanilla. Beat until mixed.
Beat or stir in the flour mixture. Stir in the quick-cooking rolled oats and the finely chopped apple. Shape the dough into 1-1/2-inch balls and place the balls 2 inches apart on an ungreased cookie sheet. Flatten the cookie dough slightly with the tines of a fork.
Bake the shaped cookies in a 375 degree F oven for 10 to 12 minutes or until the edges of the cookies are firm. Remove the cookies to cool on a wire rack. Makes about 40.