Pre-heat oven to 350°F. Line a 9x5-inch loaf pan with parchment paper and spray the un-lined ends with baking spray. The paper will help you lift the finished cake out of the pan.
Peel apples and remove the stem, end, and core. Cut the apples in half lengthwise, then slice into uniform paper-thin slices, ideally 1/16-inch, and at most ⅛-inch thick. I use a mandoline for this.
Make Invisible Apple Cake
In a large mixing bowl, beat eggs and sugar together until light and pale yellow.
Add milk, melted butter, and vanilla extract, and whisk until well-combined.
Sift flour, salt, and baking powder directly over the bowl into the liquid mixture and whisk together until just combined.
Add sliced apples and gently fold into the batter, making sure to separate the slices so they are all evenly coated. Use a soft, flexible spatula, or better yet, use your hands.
Layer the coated apples into the loaf pan, a few slices at a time, arranging them around the edge of the pan with the cut sides on the outermost edges. Doing this by hand will ensure that the apple slices are flat. Save 10-12 slices of the same size to create a uniform overlapping pattern as the last layer on top.
Pour any remaining batter over the apple slices in the loaf pan. Gently press down on the apples and lightly tap the pan to pop out any air bubbles and help the apples settle into place.
Bake, rotating pan halfway through, until top is golden brown and a tester inserted in the center slips in and out easily, 60 to 70 minutes. I bake mine for the full 70 minutes.
Remove cake from oven. Run a small knife with a thin blade along the unlined edges, and cool in pan for about 10 minutes. Carefully remove the cake from the pan using the parchment paper as two handles and place on a wire rack to cool completely for about 1 hour. DO NOT CUT into the cake until completely cooled or the layer will slip apart.
To Serve Invisible Apple Cake
To serve, use a serrated knife to carefully cut 1-inch wide slice. Instead of pressing down which will squash the apple slices out the side, or using a back-and-forth sawing motion to cut which might pull the layers apart, use a single slicing motion in one direction, remove the knife, and slice again.