PREHEAT oven to 375° F. Line baking sheets with parchment paper or lightly grease.
COMBINE flour, almond meal, cinnamon, salt, baking soda, nutmeg, allspice and ginger in small bowl. Beat butter, brown sugar and granulated sugar in large mixer bowl on medium speed until well combined. Reduce speed to low. Add applesauce and vanilla extract; mix until well combined. Increase speed to medium. Add flour mixture; mix until combined and fluffy. Stir in oats, apple pieces and morsels. Drop by heaping tablespoons about 2 inches apart on prepared baking sheets. Using a fork, flatten each dollop into a disk shape.
BAKE for 12 to 13 minutes or until they just start to turn golden brown and just set in center. The centers will be fairly firm. Cool on baking sheets for 2 minutes; remove to wire racks to cool completely.
*Almond meal or flour is made of ground-up almonds. Almond meal can be made with either whole or blanched almonds (no skin); almond flour is made with blanched almonds. Found in health food stores, the meal can also be made at home. Place small amounts in your blender or food processor and pulse until the almonds are meal. If you go too far, you will have almond butter or paste! If you do not want to use almond meal, substitute whole-wheat or all-purpose flour.