Adjust an oven rack to the center position and preheat oven to 350 degrees. Line 2 cookie sheets with parchment paper or lightly grease them.

In a mixing bowl beat together the butter and brown sugar with an electric mixer on medium speed until smooth. Add the maple syrup, applesauce, egg, and vanilla or maple extract, and beat until well blended.

Add the baking soda, salt, rolled oats, flour, and Grape-Nuts and stir just until combined.

Arrange the dough by heaping teaspoonfuls spaced 2 inches apart onto the prepared cookie sheets. Press down the cookies slightly with floured or dampened fingers.

Bake, one cookie sheet at a time in the center of the oven until lightly golden brown, 10 to 14 minutes.

Remove from the oven and cool on the cookie sheets for 2 to 3 minutes and then transfer the cookies to wire racks to cool completely.