Preheat the oven to 350°F (175°C). Line a 9x5-inch loaf pan with parchment paper, leaving overhang on the long sides, and lightly butter any exposed pan surface.
In a large bowl, whisk the eggs and ½ cup sugar for 1 to 2 minutes until pale and slightly foamy. Whisk in the melted butter, milk, heavy cream, and vanilla until smooth.
Sprinkle the flour, baking powder, and salt over the wet mixture and whisk gently just until no streaks of flour remain. The batter will look thin, which is exactly right.
Working one apple at a time, peel and core each apple, then run it across the mandoline set to 2 to 3mm. Toss the slices with the lemon juice to keep them bright.
Add all the apple slices to the bowl of batter and gently fold with a flexible spatula so each slice is coated in a thin film of batter. It will look like far too many apples, which is normal.
Transfer the coated apples to the lined loaf pan a few handfuls at a time, pressing each addition down gently to compress the layers and remove air pockets. Pour any remaining batter over the top and smooth flat.
Sprinkle the reserved 1 tablespoon of sugar evenly over the top. Bake for 1 hour to 1 hour 15 minutes, until the top is deep golden brown and the center is set with no wet jiggle. Tent with foil if the top darkens too fast.
Let the cake cool in the pan for about 20 minutes, then use the parchment overhang to lift it onto a rack and cool completely, at least 2 hours, before slicing.