Preheat oven to 350. Line a 9×13-inch baking pan with foil or parchment paper, making sure the edges extend over the edges of the pan for easy removal. Place prepared pan in the freezer.
Sift together flour, baking soda, salt, cinnamon, and nutmeg. Stir in the oats and sugar. In a separate small bowl, stir together the melted butter, eggs and vanilla. Mix liquid mixture into the oat mixture.
Press half of the dough into the prepared pan. Set aside.
Place the remaining dough between two 15-inch lengths of wax paper. Roll out into a 9×13-inch rectangle. Slide a flat cookie sheet under the dough and wax paper and transfer it to the freezer for a few minutes.
Peel, quarter and core the apples. Cut each quarter lengthwise into five or six slices. Place the apple slices in rows, each slice slightly overlapping the last, on top of the bottom layer of dough.
Remove the rolled-out rectangle from the freezer. Peel off the top piece of paper and turn the dough over the apples. Remove the remaining paper and press down on the edges of the dough to seal it.
Bake for 25 to 30 minutes. Cool in the pan. Lift cake out using the edges of the foil and cut into squares or bars. Maida says that chilling makes the bars easier to cut and also that they freeze well!