1 cup mild extra-virgin olive oil, plus more for pan
1/2 cup plus 2 tsp. (100 g plus 10 g) granulated sugar, plus more for pan
2 sweet apples, such as Golden Delicious or Gala
1 tsp. ground cinnamon
1/2 tsp. freshly ground black pepper
1/2 tsp. ground cardamom
1/2 tsp. ground ginger
1 1/2 cups (185 g) all-purpose flour
2 tsp. baking powder
2 large eggs
2 egg yolks
1/2 cup (100 g) (packed) brown sugar
1 tsp. vanilla extract
1/2 tsp. kosher salt
Preheat oven to 350°F. Pour about 1 Tbsp. oil into a 9x5" loaf pan and coat bottom and sides with fingertips. Sprinkle granulated sugar onto sides and bottom of pan to lightly coat.
Grate apples, peel and all, on the large holes of a box grater. Gather apples in a clean kitchen towel and wring out excess liquid. Be aggressive! You want them as dry as possible when they go into the batter.
Whisk cinnamon, pepper, cardamom, and ginger in a medium bowl. Transfer 1/4 tsp. spice mixture to a small bowl; 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 1/2 cup granulated sugar in a large bowl. Continue whisking vigorously until lightened in color 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 flexible rubber spatula just until combined, taking care not to overmix.
Fluff up grated apples and scatter over batter. Gently fold to incorporate.
Transfer batter to prepared pan; smooth top. Add 2 tsp. granulated sugar to reserved spice mixture and mix to combine. Sprinkle spiced sugar evenly over top of batter.
Bake cake until deep golden brown and a tester inserted into the center comes out clean, 60–70 minutes. Let cake cool in pan. Run a butter knife or offset spatula along edge of cake to loosen and invert onto a platter.
Do Ahead: Cake can be made 3 days ahead (the flavor gets slightly more intense each day). Store in an airtight container at room temperature.