Preheat oven to 350°F.
Pour about 1 tbsp oil into a 9x5" loaf pan and coat bottom and sides with a brush.
Sprinkle granulated sugar on the sides and bottom of pan to lightly coat.
Grate unpeeled apples on the large holes of a box grater.
Gather apples in a clean kitchen towel and wring out excess liquid. Get them as dry as possible before they go into the batter.
Whisk cinnamon, pepper, cardamom and ginger in a medium bowl.
Transfer ¼ tsp spice mixture to a small bowl and set aside.
Add flour and baking powder to remaining spice mixture and whisk to combine.
Whisk together eggs, egg yolks, brown sugar, vanilla, salt and ½ cup granulated sugar in a large bowl. Continue whisking vigorously until lightened in colour and thickened.
Whisking with one hand and pouring with the other, slowly stream 1 cup oil into egg mixture until combined.
Gently fold flour mixture into whipped eggs with a rubber spatula until just combined, taking care not to overmix.
Fluff up grated apples and scatter over batter. Gently fold to incorporate.
Transfer batter to prepared pan and smooth top.
Add 2 tsp granulated sugar to reserved spice mixture and mix to combine. Sprinkle spiced sugar evenly over top of batter.
Bake until deep golden brown and a tester inserted into the centre comes out clean, 60–70 minutes.
Let cake cool in pan. Run an offset spatula along edge of cake to loosen and invert onto a platter.
Store in an airtight container at room temperature.