Prepare pan: (See Note at the end about loaf pan size.) Coat the short ends of a loaf pan with butter or nonstick spray. Line the bottom and two long sides of the pan with a piece of parchment paper. Place loaf pan on a rimmed baking sheet, just in case there’s overflow.
Preheat oven to 375 degrees
Prepare apples: Peel and core your apples, then slice them very thin (about 1/8-inch or 1/3-cm thick). A mandoline works great for this. No mandoline? A Chef's knife works too. Place sliced apples in a large bowl and gently toss with lemon juice.
Make cake batter: Melt butter in a medium bowl. Whisk in sugar and salt, then eggs and vanilla. Whisk in flour until smooth, then add milk or half and half. Pour batter over sliced apples, then gently stir and turn the apples a few times so they’re evenly coated. Use your hands or a spatula to mix. Try not to break the apples.
Assemble cake Smitten Kitchen style: Using your hands is easiest for this. Push about a dozen full slices to the side of the bowl for the final layer. Arrange the remaining apple slices slightly overlapped around the prepared loaf pan, pushing the straight edges against the sides for the neatest appearance. Use any smaller or broken apples to fill any center gap. Pour excess batter over it push the pieces around until it’s level. Tap the pan on the counter a few times to release any trapped air bubbles. Use the reserved apple slices to decorate the top, fanning them into a flower pattern if you wish or overlapping columns of apples looks great too.
Or the David Lebovitz way: Carefully, pour apples and custard into loaf pan. Start with a third of the apples, make sure each layer is level and flat, before adding the next. Pour and excess batter on top. This is much more rustic-looking. In place of the SK glaze finish, sprinkle 3 tablespoons of light brown sugar or turbinado sugar on top of cake before baking.
Bake the cake: For 60 to 70 minutes, or until a toothpick or skewer inserted into the center of the cake comes out batter-free and doesn’t feel like it’s spearing any raw/crunchy apples. Transfer to a cooling rack for 5 minutes. iI you didn't sprinkle with brown sugar a la David's style, then brush top with warmed apricot preserves. Let cool completely in the pan. The cake will be puffed at first, and will settle flat as it cools. If the top is browns too quickly, cover it with foil and continue to bake.
Serve: Once cooled to room temperature, use a knife to loosen the cake from the short ends of the pan. Use the sides of parchment paper around the longer sides of the cake to help lift it out of the pan. Transfer to a serving plate. Cut into slices, the layers look pretty neat. Dust with powdered sugar, if using. OR serve with Creme Anglaise or Caramel sauce. Cheater's hint. You can let your vanilla ice cream sit out and melt, then use that as a sauce or TJ's Fleur de Sel Caramel Sauce works. It's delish.